Edit Profile (opens in new tab) Parthasarathy, Kalyanapuram Rangachari Co-Author Distance Author ID: parthasarathy.kalyanapuram-rangachari Published as: Parthasarathy, K. R.; Parthasarathy, Kalyanapuram Rangachari; Parthasarathy, Kalyanapuram R. more...less External Links: MGP · Wikidata · Math-Net.Ru · GND · IdRef Documents Indexed: 173 Publications since 1960, including 17 Books and 2 Additional arXiv Preprints 7 Contributions as Editor · 3 Further Contributions Biographic References: 1 Publication Co-Authors: 37 Co-Authors with 78 Joint Publications 928 Co-Co-Authors all top 5 Co-Authors 97 single-authored 18 Hudson, Robin Lyth 13 Sinha, Kalyan B. 10 Varadhan, S. R. Srinivasa 7 Lindsay, J. Martin 6 Bhatia, Rajendra 6 Ranga Rao, R. 5 Schmidt, Klaus 4 Bhat, B. V. Rajarama 4 Bhatt, Abhay G. 4 Sengupta, Ritabrata 4 Varadarajan, Veeravalli S. 3 Ion, Patrick D. F. 2 Accardi, Luigi 2 Pulmannová, Sylvia 2 Steerneman, Ton 1 Arvind, Vikraman 1 Attal, Stéphane 1 Babbitt, Donald George 1 Bailey, Norman T. J. 1 Balasubramanian, Krishnaswami 1 Beltrametti, Enrico G. 1 Bhattacharya, P. K. 1 Bingham, Michael S. 1 Brownell, F. H. III 1 Cassinelli, Gianni 1 Devinatz, Allen 1 Disney, Ralph L. 1 Dolph, Charles L. 1 Enss, Volker 1 Ewens, Warren J. 1 Fioresi, Rita 1 Gangolli, Ramesh 1 Gani, Joseph Mark 1 Ghosh, Jayanta Kumar 1 Ghosh, Sibasish 1 Goodrich, Robert Kent 1 Gupta, J. C. 1 Gupta, Ved Prakash 1 Gustafson, Karl Edwin 1 Hannan, Edward James 1 Hartman, R. L. 1 Howland, James S. 1 Jaffé, Charles 1 Johanson, G. 1 John, Tiju Cherian 1 Jones, William Branham 1 Karandikar, Rajeeva Laxman 1 Keilson, Julian 1 Kendall, David George 1 Klink, William H. 1 Kochubeĭ, Anatoliĭ Naumovych 1 Kurur, Piyush P. 1 Mandayam, Prabha 1 Manjunath, B. G. 1 Marchand, Jean-Paul 1 Misra, Baidyanath 1 Mitra, Sujit Kumar 1 Mohari, Anilesh 1 Neuts, Marcel Fernand 1 Paulsen, Vern Ival 1 Pisier, Gilles 1 Plymen, Roger J. 1 Prabhu, Narahari Umanath 1 Ramm, Alexander G. 1 Reinhardt, William P. 1 Sazonov, Vyacheslav Vasil’evich 1 Schechter, Martin 1 Schroeck, Franklin E. jun. 1 Seddighin, Morteza 1 Shirts, Randall B. 1 Sigal, Israel Michael 1 Simon, Barry 1 Singh, Ajit Iqbal 1 Solomon, Herbert 1 Sunder, Viakalathur S. 1 Syski, Ryszard 1 Tadjeran, H. 1 Thron, Wolfgang Joseph 1 Ton-That, Tuong 1 Tretkoff, Paula 1 Tweedie, Richard Lewis 1 Usha Devi, A. R. 1 Vere-Jones, David 1 Watson, Geoffrey S. 1 Weder, Ricardo A. 1 Whittle, Peter 1 Winter, Andreas 1 Xia, Daoxing all top 5 Serials 12 Sankhyā. Series A. Methods and Techniques 9 Infinite Dimensional Analysis, Quantum Probability and Related Topics 8 Communications in Mathematical Physics 6 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 5 Teoriya Veroyatnosteĭ i eë Primeneniya 5 Journal of Functional Analysis 5 Texts and Readings in Mathematics 4 Journal of Mathematical Physics 3 Letters in Mathematical Physics 3 Reviews in Mathematical Physics 3 Bulletin of the London Mathematical Society 3 Illinois Journal of Mathematics 3 The Mathematics Student 2 Indian Journal of Pure & Applied Mathematics 2 Journal of Applied Probability 2 Proceedings of the American Mathematical Society 2 Transactions of the American Mathematical Society 2 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 2 Journal of the London Mathematical Society 2 ISI Lecture Notes 2 Lecture Notes in Mathematics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Periodica Mathematica Hungarica 1 Acta Mathematica 1 Journal of Multivariate Analysis 1 Journal of Statistical Planning and Inference 1 Mathematische Zeitschrift 1 Monatshefte für Mathematik 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Combinatorica 1 Probability and Mathematical Statistics 1 Acta Applicandae Mathematicae 1 Probability Theory and Related Fields 1 Journal of the Australian Mathematical Society. Series A 1 Linear Algebra and its Applications 1 Stochastic Processes and their Applications 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Bollettino della Unione Matemàtica Italiana. Serie VI. A 1 Expositiones Mathematicae 1 Tatra Mountains Mathematical Publications 1 Journal of Applied Analysis 1 Annals of Mathematics. Second Series 1 Bulletin of the American Mathematical Society 1 Applied Probability 1 Lectures on Mathematics and Physics. Mathematics. Tata Institute of Fundamental Research 1 Lecture Notes in Physics 1 Monographs in Mathematics 1 Unitext 1 Communications on Stochastic Analysis 1 Quantum Information & Computation 1 Annals of Mathematical Statistics 1 Sankhyā. Series A 1 Mathematics Newsletter 1 Modern Birkhäuser Classics all top 5 Fields 99 Probability theory and stochastic processes (60-XX) 92 Quantum theory (81-XX) 55 Functional analysis (46-XX) 23 Operator theory (47-XX) 13 Information and communication theory, circuits (94-XX) 11 History and biography (01-XX) 11 Topological groups, Lie groups (22-XX) 10 Measure and integration (28-XX) 9 Statistics (62-XX) 8 Group theory and generalizations (20-XX) 7 Linear and multilinear algebra; matrix theory (15-XX) 7 Statistical mechanics, structure of matter (82-XX) 6 Abstract harmonic analysis (43-XX) 4 Nonassociative rings and algebras (17-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 3 General and overarching topics; collections (00-XX) 3 Combinatorics (05-XX) 3 Functions of a complex variable (30-XX) 3 Partial differential equations (35-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 General topology (54-XX) 1 Number theory (11-XX) 1 Real functions (26-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-XX) 1 Integral transforms, operational calculus (44-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 120 Publications have been cited 2,979 times in 2,481 Documents Cited by ▼ Year ▼ Probability measures on metric spaces. Zbl 0153.19101 Parthasarathy, K. R. 1,135 1967 Quantum Ito’s formula and stochastic evolutions. Zbl 0546.60058 Hudson, R. L.; Parthasarathy, K. R. 379 1984 An introduction to quantum stochastic calculus. Zbl 0751.60046 Parthasarathy, K. R. 300 1992 Representation of complex semi-simple Lie groups and Lie algebras. Zbl 0177.18004 Parthasarathy, K. R.; Ranga Rao, R.; Varadarajan, V. S. 99 1967 Probability measures on metric spaces. Reprint of the 1967 original. Zbl 1188.60001 Parthasarathy, K. R. 93 2005 Positive definite kernels, continuous tensor products, and central limit theorems of probability theory. Zbl 0237.43005 Parthasarathy, K. R.; Schmidt, K. 86 1972 Introduction to probability and measure. Zbl 0395.28001 Parthasarathy, K. R. 52 1977 Positive definite functions and operator inequalities. Zbl 1037.15021 Bhatia, Rajendra; Parthasarathy, K. R. 50 2000 Probability distributions on locally compact Abelian groups. Zbl 0129.10902 Parthasarathy, K. R.; Rao, R. Ranga; Varadhan, S. R. S. 42 1963 On the category of ergodic measures. Zbl 0103.28101 Parthasarathy, K. R. 36 1961 Unification of Fermion and Boson stochastic calculus. Zbl 0604.60063 Hudson, R. L.; Parthasarathy, K. R. 36 1986 On the maximal dimension of a completely entangled subspace for finite level quantum systems. Zbl 1080.46014 Parthasarathy, K. R. 31 2004 An introduction to quantum stochastic calculus. Reprint of the 1992 ed. Zbl 1338.81010 Parthasarathy, K. R. 30 2013 What is a Gaussian state? Zbl 1331.81169 Parthasarathy, K. R. 27 2010 Stochastic integral representation of bounded quantum martingales in Fock space. Zbl 0594.60059 Parthasarathy, K. R.; Sinha, K. B. 25 1986 Cohomology of power sets with applications in quantum probability. Zbl 0678.60041 Lindsay, J. M.; Parthasarathy, K. R. 24 1989 Stochastic dilations of uniformly continuous completely positive semigroups. Zbl 0541.60066 Hudson, R. L.; Parthasarathy, K. R. 23 1984 On the category of indecomposable distributions on topological groups. Zbl 0104.36205 Parthasarathy, K. R.; Ranga Rao, R.; Varadhan, S. R. S. 21 1962 Multipliers on locally compact groups. Zbl 0188.20202 Parthasarathy, K. R. 20 1969 On estimating the state of a finite level quantum system. Zbl 1077.47060 Parthasarathy, K. R. 20 2004 Extremal decision rules in quantum hypothesis testing. Zbl 1043.81512 Parthasarathy, K. R. 18 1999 Markov dilations of nonconservative dynamical semigroups and a quantum boundary theory. Zbl 0832.46060 Rajarama Bhat, B. V.; Parthasarathy, K. R. 17 1995 An entropic uncertainty principle for quantum measurements. Zbl 1192.81038 Krishna, M.; Parthasarathy, K. R. 17 2002 Time-orthogonal unitary dilations and noncommutative Feynman-Kac formulae. Zbl 0485.46038 Hudson, R. L.; Ion, P. D. F.; Parthasarathy, K. R. 15 1982 Projective unitary antiunitary representations of locally compact groups. Zbl 0186.28403 Parthasarathy, K. R. 15 1969 The functional analysis of quantum information theory. A collection of notes based on lectures by Gilles Pisier, K. R. Parthasarathy, Vern Paulsen and Andreas Winter. Zbl 1431.81007 Gupta, Ved Prakash; Mandayam, Prabha; Sunder, V. S. 15 2015 Factorisable representations of current groups and the Araki-Woods imbedding theorem. Zbl 0233.22003 Parthasarathy, K. R.; Schmidt, K. 14 1972 Introduction to probability and measure. 2nd revised ed. Zbl 1075.28001 Parthasarathy, K. R. 14 2005 Extremal quantum states in coupled systems. Zbl 1074.81045 Parthasarathy, K. R. 14 2005 On the integral representation of the rate of transmission of a stationary channel. Zbl 0100.33903 Parthasarathy, K. R. 13 1961 The symmetry group of Gaussian states in \({L}^{2}({\mathbb{R}}^{n})\). Zbl 1275.81059 Parthasarathy, Kalyanapuram R. 13 2013 Geodetic blocks of diameter three. Zbl 0554.05043 Parthasarathy, K. R.; Srinivasan, N. 11 1984 The passage from random walk to diffusion in quantum probability. II. Zbl 0771.60056 Lindsay, J. M.; Parthasarathy, K. R. 11 1988 A new method for constructing factorisable representations for current groups and current algebras. Zbl 0332.43009 Parthasarathy, K. R.; Schmidt, K. 11 1976 Square integrable martingales orthogonal to every stochastic integral. Zbl 0376.60052 Parthasarathy, K. R. 11 1978 From particle counting to Gaussian tomography. Zbl 1364.81076 Parthasarathy, K. R.; Sengupta, Ritabrata 11 2015 Symplectic dilations, Gaussian states and Gaussian channels. Zbl 1351.60040 Parthasarathy, K. R. 11 2015 Kolmogorov’s existence theorem for Markov processes in \(C^*\) algebras. Zbl 0796.60092 Bhat, B. V. Rajarama; Parthasarathy, K. R. 10 1994 On the generators of quantum stochastic flows. Zbl 0914.60033 Lindsay, J. Martin; Parthasarathy, K. R. 9 1998 A martingale characterization of canonical commutation and anticommutation relations. Zbl 0642.60032 Accardi, Luigi; Parthasarathy, K. R. 8 1988 Quantum stochastic calculus and quantum Gaussian processes. Zbl 1351.60090 Parthasarathy, K. R. 8 2015 On the derivation of the Schrödinger equation in a Riemannian manifold. Zbl 0176.26301 Parthasarathy, K. R. 7 1968 Infinitely divisible representations and positive definite functions on a compact group. Zbl 0189.55101 Parthasarathy, K. R. 7 1970 Stable positive definite functions. Zbl 0314.43004 Parthasarathy, K. R.; Schmidt, K. 7 1975 Extension of stationary stochastic processes. Zbl 0138.11001 Parthasarathy, K. R.; Varadhan, S. R. S. 6 1964 On a class of time inhomogeneous nonsingular flows and Schrödinger operators. Zbl 0469.58006 Parthasarathy, Kalyanapuram Rangachari 5 1982 Some limit theorems in regression theory. Zbl 0097.34903 Parthasarathy, K. R.; Bhattacharya, P. K. 5 1961 A note on mixing processes. Zbl 0108.30702 Parthasarathy, K. R. 5 1962 Effective entropy rate and transmission of information through channels with additive random noise. Zbl 0119.34003 Parthasarathy, K. R. 5 1963 Glimpses of India’s statistical heritage. Zbl 0823.00009 5 1993 Stochastic integral representation of some quantum martingales in Fock space. Zbl 0616.46073 Hudson, R. L.; Lindsay, J. M.; Parthasarathy, K. R. 5 1986 Markov chains as Evans-Hudson diffusions in Fock space. Zbl 0699.60065 Parthasarathy, K. R.; Sinha, K. B. 5 1990 On the cohomology of a hyperfinite action. Zbl 0384.28017 Parthasarathy, K. R.; Schmidt, K. 5 1977 Eigenvalues of matrix-valued analytic maps. Zbl 0389.47009 Parthasarathy, K. R. 5 1978 Lectures on functional analysis. Part I: Perturbation by bounded operators. Zbl 0451.47020 Bhatia, Rajendra; Parthasarathy, K. R. 5 1978 Introduction to probability and measure. (Vvedenie v teoriyu veroyatnostej i teoriyu mery). Transl. from the English. Zbl 0529.28001 Parthasarathy, K. R. 4 1983 Construction of quantum diffusions. Zbl 0542.60053 Hudson, R. L.; Parthasarathy, K. R. 4 1984 Coding theorems of classical and quantum information theory. 2nd ed. Zbl 1261.94001 Parthasarathy, K. R. 4 2013 Azéma martingales with drift. Zbl 0852.60051 Parthasarathy, K. R. 4 1995 Stochastic calculus on local algebras. Zbl 0584.60075 Accardi, Luigi; Parthasarathy, K. R. 4 1985 Stop times in Fock space stochastic calculus. Zbl 0599.60044 Parthasarathy, K. R.; Sinha, Kalyan B. 4 1987 A tool in establishing total variation convergence. Zbl 0602.60005 Parthasarathy, K. R.; Steerneman, Ton 4 1985 Representation of a class of quantum martingales. II. Zbl 0641.46039 Parthasarathy, K. R.; Sinha, Kalyan B. 3 1988 Chaos map for the universal enveloping algebra of \(U(N)\). Zbl 0815.60057 Hudson, R. L.; Parthasarathy, K. R. 3 1995 Remarks on Bell’s inequality for spin correlations. Zbl 1058.82503 Balasubramanian, K.; Gupta, J. C.; Parthasarathy, K. R. 3 1998 Extreme points of the convex set of stochastic maps on a \(C^*\)-algebra. Zbl 0940.46041 Parthasarathy, K. R. 3 1998 Unification of quantum noise processes in Fock spaces. Zbl 0942.46047 Parthasarathy, K. R.; Sinha, Kalyan B. 3 1991 On the imbedding of an infinitely divisible distribution in a one- parameter convolution semigroup. Zbl 0178.21302 Parthasarathy, K. R. 3 1967 Time-orthogonal unitary dilations and noncommutative Feynman-Kac formulae. II. Zbl 0575.46053 Hudson, R. L.; Ion, P. D. F.; Parthasarathy, K. R. 3 1984 A continuous time version of Stinespring’s theorem on completely positive maps. Zbl 0743.46060 Parthasarathy, K. R. 3 1990 Comparison of completely positive maps on a \(C^*\)-algebra and a Lebesgue decomposition theorem. Zbl 0916.46049 Parthasarathy, K. R. 3 1996 Casimir chaos in a boson Fock space. Zbl 0804.60052 Hudson, R. L.; Parthasarathy, K. R. 3 1994 Exchangeable, stationary, and entangled chains of Gaussian states. Zbl 1325.81019 Parthasarathy, K. R.; Sengupta, Ritabrata 3 2015 From quantum stochastic differential equations to Gisin-Percival state diffusion. Zbl 1370.81099 Parthasarathy, K. R.; Usha Devi, A. R. 3 2017 A common parametrization for finite mode Gaussian states, their symmetries, and associated contractions with some applications. Zbl 1459.81141 John, Tiju Cherian; Parthasarathy, K. R. 3 2021 Method of formal power series in quantum stochastic calculus. Zbl 0968.60101 Hudson, R. L.; Parthasarathy, K. R.; Pulmannová, S. 2 2000 On consistency of the maximum likelihood method in testing multiple quantum hypotheses. Zbl 1074.81536 Parthasarathy, K. R. 2 2000 On extremal correlations. Zbl 1005.62061 Parthasarathy, K. R. 2 2002 Flows of quantum noise. Zbl 0956.60068 Hudson, Robin L.; Lindsay, J. Martin; Parthasarathy, K. R. 2 1998 A probabilistic proof of Bochner’s theorem on positive definite functions. Zbl 0164.19302 Bingham, M. S.; Parthasarathy, K. R. 2 1968 Representations of complex semi-simple Lie groups and Lie algebras. Zbl 0178.16802 Parthasarathy, K. R.; Ranga Rao, R.; Varadarajan, V. S. 2 1966 Probability theory on the closed subspaces of a Hilbert space. Zbl 0321.60090 Parthasarathy, K. R. 2 1970 The craft of probabilistic modelling. A collection of personal accounts. Zbl 0605.60006 2 1986 Quantum stochastic calculus. Zbl 0606.46038 Parthasarathy, K. R. 2 1986 One parameter semigroups of completely positive maps on groups arising from quantum stochastic differential equations. Zbl 0607.46040 Parthasarathy, K. R. 2 1986 A generalised Biane process. Zbl 0701.60104 Parthasarathy, K. R. 2 1990 Quantum Ito’s formula. Zbl 0713.60066 Parthasarathy, K. R. 2 1989 Stop times in Fock space stochastic calculus. Zbl 0723.60057 Parthasarathy, K. R.; Sinha, Kalyan B. 2 1987 Central limit theorems for positive definite functions on Lie groups. Zbl 0374.60027 Parthasarathy, K. R. 2 1977 Infinitely divisible distributions in \(SL(k,\mathbb{C})\) or \(SL(k,\mathbb{R})\) may be imbedded in diadic convolution semigroups. Zbl 0395.60011 Parthasarathy, K. R. 2 1979 A quantum stochastic approach to Itô’s formula for Lévy processes. Zbl 0769.60050 Parthasarathy, Kalyanapuram Rangachari 2 1992 On a class of generalised Evans-Hudson flows related to classical Markov processes. Zbl 0797.60073 Mohari, A.; Parthasarathy, K. R. 2 1992 A note on McMillan’s theorem for countable alphabets. Zbl 0199.21401 Parthasarathy, K. R. 2 1964 Non-stabilizer quantum codes from Abelian subgroups of the error group. Zbl 1213.81048 Arvind, V.; Kurur, P. P.; Parthasarathy, K. R. 2 2004 Corrigendum to: “A tool in establishing total variation convergence”. Zbl 0637.60004 Parthasarathy, K. R.; Steerneman, Ton 1 1987 A unified approach to classical, bosonic and fermionic Brownian motions. Zbl 0656.60085 Parthasarathy, K. R. 1 1988 The passage from random walk to diffusion in quantum probability. Zbl 0662.60083 Parthasarathy, K. R. 1 1988 Coding theorems of classical and quantum information theory. Zbl 1133.94003 Parthasarathy, K. R. 1 2007 Quantum mechanics in mathematics, chemistry, and physics. (Proceedings of a Special Session in Mathematical Physics organized as a part of the 774th Meeting of the American Mathematical Society, held March 27-29, 1980, in Boulder, Colorado). Zbl 0489.46053 1 1981 A stochastic Dyson series expansion. Zbl 0509.60065 Parthasarathy, K. R.; Sinha, K. B. 1 1983 Twisted convolution quantum information channels, one-parameter semigroups and their generators. Zbl 1518.81025 Parthasarathy, K. R. 1 2022 A common parametrization for finite mode Gaussian states, their symmetries, and associated contractions with some applications. Zbl 1459.81141 John, Tiju Cherian; Parthasarathy, K. R. 3 2021 Optimal quantum tomography with constrained measurements arising from unitary bases. Zbl 1483.81023 Chaturvedi, S.; Ghosh, S.; Parthasarathy, K. R.; Singh, Ajit Iqbal 1 2021 From quantum stochastic differential equations to Gisin-Percival state diffusion. Zbl 1370.81099 Parthasarathy, K. R.; Usha Devi, A. R. 3 2017 On the equivalence of separability and extendability of quantum states. Zbl 1370.81014 Bhat, B. V. Rajarama; Parthasarathy, K. R.; Sengupta, Ritabrata 1 2017 The functional analysis of quantum information theory. A collection of notes based on lectures by Gilles Pisier, K. R. Parthasarathy, Vern Paulsen and Andreas Winter. Zbl 1431.81007 Gupta, Ved Prakash; Mandayam, Prabha; Sunder, V. S. 15 2015 From particle counting to Gaussian tomography. Zbl 1364.81076 Parthasarathy, K. R.; Sengupta, Ritabrata 11 2015 Symplectic dilations, Gaussian states and Gaussian channels. Zbl 1351.60040 Parthasarathy, K. R. 11 2015 Quantum stochastic calculus and quantum Gaussian processes. Zbl 1351.60090 Parthasarathy, K. R. 8 2015 Exchangeable, stationary, and entangled chains of Gaussian states. Zbl 1325.81019 Parthasarathy, K. R.; Sengupta, Ritabrata 3 2015 An introduction to quantum stochastic calculus. Reprint of the 1992 ed. Zbl 1338.81010 Parthasarathy, K. R. 30 2013 The symmetry group of Gaussian states in \({L}^{2}({\mathbb{R}}^{n})\). Zbl 1275.81059 Parthasarathy, Kalyanapuram R. 13 2013 Coding theorems of classical and quantum information theory. 2nd ed. Zbl 1261.94001 Parthasarathy, K. R. 4 2013 Probability distributions on locally compact abelian groups. Zbl 1316.60025 Parthasarathy, K. R.; Ranga Rao, R.; Varadhan, S. R. S. 1 2012 A note on Gaussian distributions in \(\mathbb R^n\). Zbl 1270.60025 Manjunath, B. G.; Parthasarathy, K. R. 1 2012 Collected papers. Volume IV: Particle systems and their large deviations. Edited by Rajendra Bhatia, Abhay Bhatt and K. R. Parthasarathy. Zbl 1311.82004 Varadhan, S. R. S. 1 2012 What is a Gaussian state? Zbl 1331.81169 Parthasarathy, K. R. 27 2010 Coding theorems of classical and quantum information theory. Zbl 1133.94003 Parthasarathy, K. R. 1 2007 Probability measures on metric spaces. Reprint of the 1967 original. Zbl 1188.60001 Parthasarathy, K. R. 93 2005 Introduction to probability and measure. 2nd revised ed. Zbl 1075.28001 Parthasarathy, K. R. 14 2005 Extremal quantum states in coupled systems. Zbl 1074.81045 Parthasarathy, K. R. 14 2005 Mathematical foundations of quantum mechanics. Revised with the assistance of M. Krishna. Zbl 1122.81002 Parthasarathy, K. R. 1 2005 On the maximal dimension of a completely entangled subspace for finite level quantum systems. Zbl 1080.46014 Parthasarathy, K. R. 31 2004 On estimating the state of a finite level quantum system. Zbl 1077.47060 Parthasarathy, K. R. 20 2004 Non-stabilizer quantum codes from Abelian subgroups of the error group. Zbl 1213.81048 Arvind, V.; Kurur, P. P.; Parthasarathy, K. R. 2 2004 Quantum probability and strong quantum Markov processes. Zbl 1087.81035 Parthasarathy, K. R. 1 2003 An entropic uncertainty principle for quantum measurements. Zbl 1192.81038 Krishna, M.; Parthasarathy, K. R. 17 2002 On extremal correlations. Zbl 1005.62061 Parthasarathy, K. R. 2 2002 An inducing construction of quantum codes from classical error correcting codes. Zbl 1012.81010 Parthasarathy, K. R. 1 2001 Positive definite functions and operator inequalities. Zbl 1037.15021 Bhatia, Rajendra; Parthasarathy, K. R. 50 2000 Method of formal power series in quantum stochastic calculus. Zbl 0968.60101 Hudson, R. L.; Parthasarathy, K. R.; Pulmannová, S. 2 2000 On consistency of the maximum likelihood method in testing multiple quantum hypotheses. Zbl 1074.81536 Parthasarathy, K. R. 2 2000 Extremal decision rules in quantum hypothesis testing. Zbl 1043.81512 Parthasarathy, K. R. 18 1999 Quantum Markov processes with a Christensen-Evans generator in a von Neumann algebra. Zbl 0956.46047 Parthasarathy, K. R.; Sinha, K. B. 1 1999 On the generators of quantum stochastic flows. Zbl 0914.60033 Lindsay, J. Martin; Parthasarathy, K. R. 9 1998 Remarks on Bell’s inequality for spin correlations. Zbl 1058.82503 Balasubramanian, K.; Gupta, J. C.; Parthasarathy, K. R. 3 1998 Extreme points of the convex set of stochastic maps on a \(C^*\)-algebra. Zbl 0940.46041 Parthasarathy, K. R. 3 1998 Flows of quantum noise. Zbl 0956.60068 Hudson, Robin L.; Lindsay, J. Martin; Parthasarathy, K. R. 2 1998 Comparison of completely positive maps on a \(C^*\)-algebra and a Lebesgue decomposition theorem. Zbl 0916.46049 Parthasarathy, K. R. 3 1996 Strong Markov processes and the Dirichlet problem in von Neumann algebras. Zbl 0926.60059 Attal, S.; Parthasarathy, K. R. 1 1996 Positivity and contractivity of quantum stochastic flows. Zbl 0919.60092 Lindsay, J. Martin; Parthasarathy, K. R. 1 1996 Markov dilations of nonconservative dynamical semigroups and a quantum boundary theory. Zbl 0832.46060 Rajarama Bhat, B. V.; Parthasarathy, K. R. 17 1995 Azéma martingales with drift. Zbl 0852.60051 Parthasarathy, K. R. 4 1995 Chaos map for the universal enveloping algebra of \(U(N)\). Zbl 0815.60057 Hudson, R. L.; Parthasarathy, K. R. 3 1995 Kolmogorov’s existence theorem for Markov processes in \(C^*\) algebras. Zbl 0796.60092 Bhat, B. V. Rajarama; Parthasarathy, K. R. 10 1994 Casimir chaos in a boson Fock space. Zbl 0804.60052 Hudson, R. L.; Parthasarathy, K. R. 3 1994 Glimpses of India’s statistical heritage. Zbl 0823.00009 5 1993 The Casimir chaos map for \(U(N)\). Zbl 0798.60068 Hudson, R. L.; Parthasarathy, K. R. 1 1993 An introduction to quantum stochastic calculus. Zbl 0751.60046 Parthasarathy, K. R. 300 1992 A quantum stochastic approach to Itô’s formula for Lévy processes. Zbl 0769.60050 Parthasarathy, Kalyanapuram Rangachari 2 1992 On a class of generalised Evans-Hudson flows related to classical Markov processes. Zbl 0797.60073 Mohari, A.; Parthasarathy, K. R. 2 1992 Unification of quantum noise processes in Fock spaces. Zbl 0942.46047 Parthasarathy, K. R.; Sinha, Kalyan B. 3 1991 Markov chains as Evans-Hudson diffusions in Fock space. Zbl 0699.60065 Parthasarathy, K. R.; Sinha, K. B. 5 1990 A continuous time version of Stinespring’s theorem on completely positive maps. Zbl 0743.46060 Parthasarathy, K. R. 3 1990 A generalised Biane process. Zbl 0701.60104 Parthasarathy, K. R. 2 1990 Cohomology of power sets with applications in quantum probability. Zbl 0678.60041 Lindsay, J. M.; Parthasarathy, K. R. 24 1989 Quantum Ito’s formula. Zbl 0713.60066 Parthasarathy, K. R. 2 1989 Some comments on quantum probability. Zbl 0751.46038 Parthasarathy, K. R. 1 1989 The passage from random walk to diffusion in quantum probability. II. Zbl 0771.60056 Lindsay, J. M.; Parthasarathy, K. R. 11 1988 A martingale characterization of canonical commutation and anticommutation relations. Zbl 0642.60032 Accardi, Luigi; Parthasarathy, K. R. 8 1988 Representation of a class of quantum martingales. II. Zbl 0641.46039 Parthasarathy, K. R.; Sinha, Kalyan B. 3 1988 A unified approach to classical, bosonic and fermionic Brownian motions. Zbl 0656.60085 Parthasarathy, K. R. 1 1988 The passage from random walk to diffusion in quantum probability. Zbl 0662.60083 Parthasarathy, K. R. 1 1988 Stop times in Fock space stochastic calculus. Zbl 0599.60044 Parthasarathy, K. R.; Sinha, Kalyan B. 4 1987 Stop times in Fock space stochastic calculus. Zbl 0723.60057 Parthasarathy, K. R.; Sinha, Kalyan B. 2 1987 Corrigendum to: “A tool in establishing total variation convergence”. Zbl 0637.60004 Parthasarathy, K. R.; Steerneman, Ton 1 1987 Unification of Fermion and Boson stochastic calculus. Zbl 0604.60063 Hudson, R. L.; Parthasarathy, K. R. 36 1986 Stochastic integral representation of bounded quantum martingales in Fock space. Zbl 0594.60059 Parthasarathy, K. R.; Sinha, K. B. 25 1986 Stochastic integral representation of some quantum martingales in Fock space. Zbl 0616.46073 Hudson, R. L.; Lindsay, J. M.; Parthasarathy, K. R. 5 1986 The craft of probabilistic modelling. A collection of personal accounts. Zbl 0605.60006 2 1986 Quantum stochastic calculus. Zbl 0606.46038 Parthasarathy, K. R. 2 1986 One parameter semigroups of completely positive maps on groups arising from quantum stochastic differential equations. Zbl 0607.46040 Parthasarathy, K. R. 2 1986 Stochastic calculus on local algebras. Zbl 0584.60075 Accardi, Luigi; Parthasarathy, K. R. 4 1985 A tool in establishing total variation convergence. Zbl 0602.60005 Parthasarathy, K. R.; Steerneman, Ton 4 1985 Quantum Ito’s formula and stochastic evolutions. Zbl 0546.60058 Hudson, R. L.; Parthasarathy, K. R. 379 1984 Stochastic dilations of uniformly continuous completely positive semigroups. Zbl 0541.60066 Hudson, R. L.; Parthasarathy, K. R. 23 1984 Geodetic blocks of diameter three. Zbl 0554.05043 Parthasarathy, K. R.; Srinivasan, N. 11 1984 Construction of quantum diffusions. Zbl 0542.60053 Hudson, R. L.; Parthasarathy, K. R. 4 1984 Time-orthogonal unitary dilations and noncommutative Feynman-Kac formulae. II. Zbl 0575.46053 Hudson, R. L.; Ion, P. D. F.; Parthasarathy, K. R. 3 1984 Generalised Weyl operators. Zbl 0551.60062 Hudson, R. L.; Parthasarathy, K. R. 1 1984 A remark on the integration of Schrödinger equation using quantum Itô’s formula. Zbl 0566.60064 Parthasarathy, K. R. 1 1984 Introduction to probability and measure. (Vvedenie v teoriyu veroyatnostej i teoriyu mery). Transl. from the English. Zbl 0529.28001 Parthasarathy, K. R. 4 1983 A stochastic Dyson series expansion. Zbl 0509.60065 Parthasarathy, K. R.; Sinha, K. B. 1 1983 Towards a theory of noncommutative semimartingales adapted to Brownian motion and a quantum Ito’s formula. Zbl 0514.60053 Hudson, R. L.; Karandikar, R. L.; Parthasarathy, K. R. 1 1983 Time-orthogonal unitary dilations and noncommutative Feynman-Kac formulae. Zbl 0485.46038 Hudson, R. L.; Ion, P. D. F.; Parthasarathy, K. R. 15 1982 On a class of time inhomogeneous nonsingular flows and Schrödinger operators. Zbl 0469.58006 Parthasarathy, Kalyanapuram Rangachari 5 1982 Quantum mechanics in mathematics, chemistry, and physics. (Proceedings of a Special Session in Mathematical Physics organized as a part of the 774th Meeting of the American Mathematical Society, held March 27-29, 1980, in Boulder, Colorado). Zbl 0489.46053 1 1981 Infinitely divisible distributions in \(SL(k,\mathbb{C})\) or \(SL(k,\mathbb{R})\) may be imbedded in diadic convolution semigroups. Zbl 0395.60011 Parthasarathy, K. R. 2 1979 Square integrable martingales orthogonal to every stochastic integral. Zbl 0376.60052 Parthasarathy, K. R. 11 1978 Eigenvalues of matrix-valued analytic maps. Zbl 0389.47009 Parthasarathy, K. R. 5 1978 Lectures on functional analysis. Part I: Perturbation by bounded operators. Zbl 0451.47020 Bhatia, Rajendra; Parthasarathy, K. R. 5 1978 Introduction to probability and measure. Zbl 0395.28001 Parthasarathy, K. R. 52 1977 On the cohomology of a hyperfinite action. Zbl 0384.28017 Parthasarathy, K. R.; Schmidt, K. 5 1977 Central limit theorems for positive definite functions on Lie groups. Zbl 0374.60027 Parthasarathy, K. R. 2 1977 A new method for constructing factorisable representations for current groups and current algebras. Zbl 0332.43009 Parthasarathy, K. R.; Schmidt, K. 11 1976 Stable positive definite functions. Zbl 0314.43004 Parthasarathy, K. R.; Schmidt, K. 7 1975 Every completely stable distribution is normal. Zbl 0275.60024 Parthasarathy, K. R. 1 1973 On the imbedding of an infinitely divisible distribution in a one parameter convolution semigroup. Zbl 0276.60023 Parthasarathy, K. R. 1 1973 Positive definite kernels, continuous tensor products, and central limit theorems of probability theory. Zbl 0237.43005 Parthasarathy, K. R.; Schmidt, K. 86 1972 Factorisable representations of current groups and the Araki-Woods imbedding theorem. Zbl 0233.22003 Parthasarathy, K. R.; Schmidt, K. 14 1972 ...and 20 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,465 Authors 37 Gough, John E. 33 Parthasarathy, Kalyanapuram Rangachari 30 Petersen, Ian Richard 28 Accardi, Luigi 27 Fel’dman, Gennadiĭ Mikhaĭlovich 25 Fagnola, Franco 25 Hudson, Robin Lyth 25 Lindsay, J. Martin 20 Belavkin, Viacheslav 20 Ji, Un Cig 20 Wang, Caishi 18 Albeverio, Sergio A. 18 James, Matthew R. 18 Jørgensen, Palle E. T. 17 Applebaum, David B. 15 Ayoola, Ezekiel O. 15 Prakasa Rao, B. L. S. 15 Sinha, Kalyan B. 14 Bhatia, Rajendra 14 Röckner, Michael 14 Schürmann, Michael 13 Bhat, B. V. Rajarama 13 Dong, Chao-Ping 13 Kondrat’yev, Yuriĭ Grygorovych 13 Kozitsky, Yuri Vasil’evich 13 Vladimirov, Igor G. 11 Kholevo, Aleksandr Semënovich 11 Jurek, Zbigniew J. 11 Nurdin, Hendra Ishwara 11 Schmidt, Klaus 10 Barchielli, Alberto 10 Lee, Keonhee 10 Lu, Yun Gang 10 Morales Rojas, Carlos Arnoldo 10 Ostaszewski, Adam J. 10 Sun, Yeneng 9 Doberkat, Ernst-Erich 9 Joseph, Anthony 9 Majumdar, Suman 9 Shirokov, Maksim Evgen’evich 9 Skeide, Michael 9 Umanità, Veronica 9 Zhang, Guofeng 8 Chari, Vyjayanthi 8 Feinberg, Eugene Aleksandrovich 8 Gliklikh, Yuriĭ Evgen’evich 8 Kasyanov, Pavlo O. 8 Kosaki, Hideki 8 Liebscher, Volkmar 8 Lowen, Robert 8 Nowak, Andrzej S. 8 Obata, Nobuaki 8 Rebolledo Berroeta, Rolando 8 Shah, Riddhi 8 Speicher, Roland 8 Yüksel, Serdar 7 Attal, Stéphane 7 Belton, Alexander C. R. 7 Bingham, Nicholas Hugh 7 Dani, Shrikrishna Gopalrao 7 Haapasalo, Erkka Theodor 7 Huang, Zhiyuan 7 Lytvynov, Eugene W. 7 McCrudden, Michael 7 Pellegrini, Clément 7 Pellonpää, Juha-Pekka 7 Siebert, Eberhard 7 Zgurovsky, Mikhail Z. 6 Brzeźniak, Zdzisław 6 Greenstein, Jacob 6 Hazod, Wilfried 6 Kratschmer, Volker 6 Nikeghbali, Ashkan 6 Olsen, Lars Ole Ronnow 6 Oppel, Ulrich G. 6 Papageorgiou, Nikolaos S. 6 Rawla, Mandeep Singh 6 Sasso, Emanuela 6 Skalski, Adam G. 6 Stochel, Jan 6 Šujan, Štefan 6 Terán, Pedro 6 Tortrat, Albert 6 Vershik, Anatoliĭ Moiseevich 6 Worrell, James B. 5 Agredo, Julián 5 Allen, Beth 5 Bingham, Michael S. 5 Bishop, Sheila Amina 5 Bouten, Luc 5 Boyarsky, Abraham 5 Cattaneo, U. 5 Chebotarev, Alexandr M. 5 Constantinescu, Tiberiu 5 Dąbrowska, Anita Magdalena 5 Daletskii, Alexei 5 Dhahri, Ameur 5 Dong, Daoyi 5 Ekhaguere, Godwin O. S. 5 Fichtner, Karl-Heinz ...and 2,365 more Authors all top 5 Cited in 419 Serials 107 Journal of Mathematical Physics 97 Journal of Functional Analysis 77 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 74 Infinite Dimensional Analysis, Quantum Probability and Related Topics 72 Communications in Mathematical Physics 69 Journal of Mathematical Analysis and Applications 47 Probability Theory and Related Fields 43 Journal of Multivariate Analysis 40 Transactions of the American Mathematical Society 37 Journal of Theoretical Probability 36 Stochastic Processes and their Applications 35 Journal of Economic Theory 32 Statistics & Probability Letters 32 Linear Algebra and its Applications 32 Quantum Information Processing 31 Journal of Mathematical Economics 30 Mathematische Zeitschrift 29 Stochastic Analysis and Applications 26 Mathematical Notes 26 Advances in Mathematics 24 Fuzzy Sets and Systems 23 Reports on Mathematical Physics 23 Proceedings of the American Mathematical Society 22 The Annals of Probability 22 Automatica 21 Journal of Physics A: Mathematical and Theoretical 19 Journal of Statistical Physics 19 The Annals of Statistics 19 Publications of the Research Institute for Mathematical Sciences, Kyoto University 19 SIAM Journal on Control and Optimization 19 The Annals of Applied Probability 18 Reviews in Mathematical Physics 18 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section B. Calcul des Probabilités et Statistique 18 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 17 Applied Mathematics and Optimization 17 Mathematische Nachrichten 17 Journal of Mathematical Sciences (New York) 16 Israel Journal of Mathematics 16 Letters in Mathematical Physics 16 Mathematical Proceedings of the Cambridge Philosophical Society 16 Economic Theory 14 Journal of Algebra 14 Journal of Differential Equations 13 Topology and its Applications 12 Inventiones Mathematicae 12 Journal of Soviet Mathematics 11 Lithuanian Mathematical Journal 11 Physics Letters. A 11 Journal of Statistical Planning and Inference 11 Mathematische Annalen 11 Journal of Complexity 11 Doklady Mathematics 11 Open Systems & Information Dynamics 10 International Journal of Theoretical Physics 10 Linear and Multilinear Algebra 10 International Journal of Game Theory 10 Kybernetika 10 Ergodic Theory and Dynamical Systems 10 Electronic Journal of Probability 10 New Journal of Physics 10 Electronic Journal of Statistics 9 Theory of Probability and its Applications 9 Monatshefte für Mathematik 9 Systems & Control Letters 9 Annales Henri Poincaré 9 Stochastics 8 Indian Journal of Pure & Applied Mathematics 8 Ukrainian Mathematical Journal 8 Compositio Mathematica 8 Mathematica Slovaca 8 Results in Mathematics 8 Theoretical Computer Science 8 Games and Economic Behavior 7 Integral Equations and Operator Theory 7 Journal of Econometrics 7 Journal of Optimization Theory and Applications 7 Mathematical Social Sciences 7 Acta Applicandae Mathematicae 7 Annales de l’Institut Henri Poincaré. Physique Théorique 7 Russian Journal of Mathematical Physics 7 Positivity 7 Foundations of Physics 6 Journal of the Franklin Institute 6 Acta Mathematica 6 Applied Mathematics and Computation 6 Archiv der Mathematik 6 Memoirs of the American Mathematical Society 6 Information and Computation 6 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 6 Stochastics and Stochastics Reports 6 Indagationes Mathematicae. New Series 6 Bulletin des Sciences Mathématiques 6 Finance and Stochastics 6 Journal of Machine Learning Research (JMLR) 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 Sankhyā. Series A 6 Nonlinear Analysis. Theory, Methods & Applications 5 Bulletin of the Australian Mathematical Society 5 Metrika 5 Nonlinearity ...and 319 more Serials all top 5 Cited in 61 Fields 1,136 Probability theory and stochastic processes (60-XX) 650 Quantum theory (81-XX) 392 Functional analysis (46-XX) 267 Operator theory (47-XX) 212 Measure and integration (28-XX) 212 Statistics (62-XX) 177 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 151 Topological groups, Lie groups (22-XX) 130 Dynamical systems and ergodic theory (37-XX) 119 Statistical mechanics, structure of matter (82-XX) 110 Systems theory; control (93-XX) 107 Abstract harmonic analysis (43-XX) 98 Partial differential equations (35-XX) 93 Linear and multilinear algebra; matrix theory (15-XX) 76 General topology (54-XX) 70 Nonassociative rings and algebras (17-XX) 64 Operations research, mathematical programming (90-XX) 64 Information and communication theory, circuits (94-XX) 56 Calculus of variations and optimal control; optimization (49-XX) 54 Group theory and generalizations (20-XX) 54 Numerical analysis (65-XX) 53 Computer science (68-XX) 48 Global analysis, analysis on manifolds (58-XX) 40 Combinatorics (05-XX) 34 Real functions (26-XX) 30 Ordinary differential equations (34-XX) 30 Harmonic analysis on Euclidean spaces (42-XX) 28 Fluid mechanics (76-XX) 27 Mathematical logic and foundations (03-XX) 24 Number theory (11-XX) 23 Differential geometry (53-XX) 19 Associative rings and algebras (16-XX) 16 Algebraic geometry (14-XX) 16 Category theory; homological algebra (18-XX) 15 Functions of a complex variable (30-XX) 15 Biology and other natural sciences (92-XX) 14 Potential theory (31-XX) 14 Approximations and expansions (41-XX) 14 Convex and discrete geometry (52-XX) 12 Mechanics of particles and systems (70-XX) 11 Special functions (33-XX) 10 Several complex variables and analytic spaces (32-XX) 10 Difference and functional equations (39-XX) 10 Integral transforms, operational calculus (44-XX) 8 History and biography (01-XX) 8 Order, lattices, ordered algebraic structures (06-XX) 8 Manifolds and cell complexes (57-XX) 8 Optics, electromagnetic theory (78-XX) 7 Integral equations (45-XX) 7 Relativity and gravitational theory (83-XX) 6 Geometry (51-XX) 6 Geophysics (86-XX) 5 Algebraic topology (55-XX) 4 General algebraic systems (08-XX) 4 Sequences, series, summability (40-XX) 3 Field theory and polynomials (12-XX) 3 Commutative algebra (13-XX) 2 \(K\)-theory (19-XX) 2 Mechanics of deformable solids (74-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 General and overarching topics; collections (00-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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