Edit Profile (opens in new tab) Phillips, Ralph Saul Compute Distance To: Compute Author ID: phillips.ralph-saul Published as: Phillips, R. S.; Phillips, Ralph S.; Phillips, R.; Phillips, Ralph External Links: MGP · Wikidata · GND · IdRef Documents Indexed: 127 Publications since 1940, including 6 Books 1 Further Contribution Biographic References: 1 Publication Co-Authors: 22 Co-Authors with 82 Joint Publications 671 Co-Co-Authors all top 5 Co-Authors 46 single-authored 45 Lax, Peter David 17 Sarnak, Peter Clive 4 Osgood, Brad G. 3 Bochner, Salomon 3 Hille, Einar 3 Lubotzky, Alexander 3 Sarason, Leonard 3 Synge Morawetz, Cathleen 2 Wiskott, Bettina 2 Woo, Alex C. 1 Aczél, János Dezső 1 Adams, John Frank 1 Butzer, Paul Leo 1 Crandall, Michael G. 1 Deshouillers, Jean-Marc 1 Dye, Henry Abel 1 Erdélyi, Arthur 1 Haruki, Hiroshi 1 Helson, Henry 1 Hewitt, Edwin 1 Hochstadt, Harry 1 Iwaniec, Henryk 1 Judge, Christopher M. 1 Kallman, Robert R. 1 Lorch, Edgar Raymond 1 Lumer, Gunter 1 Malin, Henry 1 Mazzeo, Rafe R. 1 Olubummo, Adegoke 1 Rickart, Charles E. 1 Rota, Gian-Carlo 1 Rudnick, Zeév 1 Shahshahani, Mehrdad M. 1 Sucheston, Louis 1 Taam, Choy-Tak 1 Tandori, Károly 1 Widder, David Vernon 1 Yosida, Kosaku 1 Zaanen, Adriaan Cornelis all top 5 Serials 19 Communications on Pure and Applied Mathematics 12 Transactions of the American Mathematical Society 8 Journal of Functional Analysis 8 Bulletin of the American Mathematical Society 5 Duke Mathematical Journal 5 Annals of Mathematics. Second Series 4 Pacific Journal of Mathematics 3 Archive for Rational Mechanics and Analysis 3 Indiana University Mathematics Journal 3 Proceedings of the American Mathematical Society 3 Geometric and Functional Analysis. GAFA 3 Proceedings of the National Academy of Sciences of the United States of America 3 Journal of Mathematics and Mechanics 2 American Journal of Mathematics 2 Colloquium Publications. American Mathematical Society 1 Journal d’Analyse Mathématique 1 Rocky Mountain Journal of Mathematics 1 Studia Mathematica 1 Mathematics of Computation 1 The Mathematical Intelligencer 1 Acta Mathematica 1 Canadian Journal of Mathematics 1 Czechoslovak Mathematical Journal 1 Integral Equations and Operator Theory 1 Inventiones Mathematicae 1 Journal of the Faculty of Science. Section I A 1 Quarterly of Applied Mathematics 1 Combinatorica 1 Journal of the American Mathematical Society 1 IMRN. International Mathematics Research Notices 1 Bulletin of the American Mathematical Society. New Series 1 Annals of Mathematics Studies 1 Mathematicians of Our Time all top 5 Fields 46 Partial differential equations (35-XX) 32 Number theory (11-XX) 21 Operator theory (47-XX) 19 Global analysis, analysis on manifolds (58-XX) 14 Functions of a complex variable (30-XX) 5 Differential geometry (53-XX) 4 Measure and integration (28-XX) 3 Integral transforms, operational calculus (44-XX) 2 History and biography (01-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Functional analysis (46-XX) 2 Geometry (51-XX) 2 Quantum theory (81-XX) 1 Combinatorics (05-XX) 1 Algebraic geometry (14-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Abstract harmonic analysis (43-XX) 1 Convex and discrete geometry (52-XX) 1 Probability theory and stochastic processes (60-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 108 Publications have been cited 4,696 times in 3,988 Documents Cited by ▼ Year ▼ Functional analysis and semigroups. Rev. ed. Zbl 0078.10004Hille, Einar; Phillips, Ralph S. 1,388 1957 Ramanujan graphs. Zbl 0661.05035Lubotzky, A.; Phillips, R.; Sarnak, P. 380 1988 Scattering theory for transport phenomena. Zbl 0214.12002Lax, P. D.; Phillips, R. S. 211 1967 Extremals of determinants of Laplacians. Zbl 0653.53022Osgood, B.; Phillips, R.; Sarnak, P. 184 1988 Local boundary conditions for dissipative symmetric linear differential operators. Zbl 0094.07502Lax, Peter; Phillips, R. S. 176 1960 Dissipative operators in a Banach space. Zbl 0101.09503Lumer, G.; Phillips, R. S. 148 1961 Dissipative operators and hyperbolic systems of partial differential equation. Zbl 0093.10001Phillips, R. S. 114 1959 Scattering theory. Zbl 0186.16301Lax, Peter D.; Phillips, Ralph S. 108 1967 Scattering theory for automorphic functions. Zbl 0362.10022Lax, Peter D.; Phillips, Ralph S. 102 1976 The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces. Zbl 0497.30036Lax, Peter D.; Phillips, Ralph S. 92 1982 On linear transformations. Zbl 0025.34202Phillips, R. S. 76 1940 On cusp forms for co-finite subgroups of PSL(2,\({\mathbb{R}})\). Zbl 0558.10017Phillips, R. S.; Sarnak, P. 71 1985 Scattering theory. Rev. ed. Zbl 0697.35004Lax, Peter D.; Phillips, Ralph S. 71 1989 An inversion formula for Laplace transforms and semi-groups of linear operators. Zbl 0059.10704Phillips, R. S. 69 1954 Functional analysis and semi-groups. 3rd printing of rev. ed. of 1957. Zbl 0392.46001Hille, Einar; Phillips, Ralph S. 66 1974 Perturbation theory for semi-groups of linear operators. Zbl 0053.08704Phillips, R. S. 62 1953 Compact isospectral sets of surfaces. Zbl 0653.53021Osgood, B.; Phillips, R.; Sarnak, P. 56 1988 Scattering theory. Zbl 0117.09104Lax, P. D.; Phillips, R. S. 56 1964 On the generation of semigroups of linear operators. Zbl 0047.11004Phillips, R. S. 53 1952 On weakly compact subsets of a Banach space. Zbl 0063.06212Phillips, R. S. 53 1943 Hecke operators and distributing points on the sphere. I. Zbl 0619.10052Lubotzky, A.; Phillips, R.; Sarnak, P. 51 1986 Exponential decay of solutions of the wave equation in the exterior of a star-shaped obstacle. Zbl 0161.08001Lax, Peter D.; Morawetz, C. S.; Phillips, R. S. 49 1963 Absolutely convergent Fourier expansions for non-commutative normed rings. Zbl 0060.27204Bochner, Salomon; Phillips, R. S. 42 1942 Hecke operators and distributing points on \(S^2\). II. Zbl 0648.10034Lubotzky, A.; Phillips, R.; Sarnak, P. 41 1987 The adjoint semi-group. Zbl 0064.11202Phillips, R. S. 39 1955 On matrices whose real linear combinations are nonsingular. Zbl 0168.02404Adams, J. F.; Lax, P. D.; Phillips, R. S. 39 1966 Scattering theory for the acoustic equation in an even number of space dimensions. Zbl 0236.35036Lax, P. D.; Phillips, R. S. 38 1972 Scattering theory for dissipative hyperbolic systems. Zbl 0295.35069Lax, P. D.; Phillips, R. S. 38 1973 Geodesics in homology classes. Zbl 0642.53050Phillips, Ralph; Sarnak, Peter 34 1987 Decaying modes for the wave equation in the exterior of an obstacle. Zbl 0181.38201Lax, Peter D.; Phillips, R. S. 33 1969 Integration in a convex linear topological space. Zbl 0022.31902Phillips, R. S. 26 1940 Elliptic-parabolic equations of the second order. Zbl 0163.34402Phillips, R. S.; Sarason, L. 23 1968 Hodge theory on hyperbolic manifolds. Zbl 0712.58006Mazzeo, Rafe; Phillips, Ralph S. 23 1990 The Weyl theorem and the deformation of discrete groups. Zbl 0614.10027Phillips, R. S.; Sarnak, P. 22 1985 Perturbation theory for the Laplacian on automorphic functions. Zbl 0743.30039Phillips, R.; Sarnak, P. 22 1992 The Laplacian for domains in hyperbolic space and limit sets of Kleinian groups. Zbl 0611.30037Phillips, R. S.; Sarnak, P. 21 1985 The circle problem in the hyperbolic plane. Zbl 0812.11035Phillips, Ralph; Rudnick, Zeév 21 1994 Translation representations for automorphic solutions of the wave equation in non-Euclidean spaces. I. Zbl 0544.10024Lax, Peter D.; Phillips, Ralph S. 20 1984 Moduli space, heights and isospectral sets of plane domains. Zbl 0677.58045Osgood, B.; Phillips, R.; Sarnak, P. 19 1989 Additive set functions and vector lattices. Zbl 0026.00105Bochner, Salomon; Phillips, R. S. 19 1941 Semi-groups of positive contraction operators. Zbl 0113.09901Phillips, R. S. 19 1962 Singular symmetric positive first order differential operators. Zbl 0141.28701Phillips, R. S.; Sarason, L. 19 1966 The Paley-Wiener theorem for the Radon transform. Zbl 0189.14803Lax, Peter D.; Phillips, R. S. 19 1970 Bessel function approximations. Zbl 0036.04001Phillips, R. S.; Malin, Henry 18 1950 The scattering of sound waves by an obstacle. Zbl 0335.35075Lax, Peter D.; Phillips, Ralph S. 17 1977 Maass cusp forms. Zbl 0566.10017Deshouillers, J.-M.; Iwaniec, H.; Phillips, R. S.; Sarnak, P. 16 1985 Translation representations for the solution of the non-Euclidean wave equation. Zbl 0425.35065Lax, Peter D.; Phillips, Ralph S. 16 1979 A note on the abstract Cauchy problem. Zbl 0058.10603Phillips, R. S. 16 1954 Scattering theory for automorphic functions. Zbl 0442.10018Lax, Peter D.; Phillips, Ralph S. 15 1980 On linear transformations. JFM 66.0554.01Phillips, R. S. 15 1940 Dissipative hyperbolic systems. Zbl 0081.31102Phillips, R. S. 15 1957 On symplectic mappings of contraction operators. Zbl 0167.13501Phillips, R. S. 15 1968 A logarithmic bound on the location of the poles of the scattering matrix. Zbl 0216.13002Lax, P. D.; Phillips, R. S. 15 1971 On one-parameter semi-groups of linear transformations. Zbl 0043.11404Phillips, R. S. 14 1951 Spectral theory for semi-groups of linear operators. Zbl 0045.21502Phillips, R. S. 14 1951 The wave equation in exterior domains. Zbl 0103.06401Lax, Peter D.; Phillips, Ralph S. 14 1962 On the extension problem for dissipative operators. Zbl 0167.13404Crandall, M. G.; Phillips, R. S. 14 1968 The spectrum of Fermat curves. Zbl 0751.11030Phillips, R.; Sarnak, P. 13 1991 A scattering theory for automorphic functions. Zbl 0297.35061Lax, P. D.; Phillips, R. S. 12 1974 The exponential decay of solutions of the wave equation in the exterior of a star-shaped obstacle. Zbl 0108.28301Lax, P. D.; Morawetz, C. S.; Phillips, R. S. 12 1962 On dissipative operators. Zbl 0181.15301Phillips, R. S. 12 1969 The acoustic equation with an indefinite energy form and the Schrödinger equation. Zbl 0186.16401Lax, P. D.; Phillips, R. S. 12 1967 Scattering theory. (Teoriya rasseyaniya). Zbl 0212.43802Lax, P. D.; Phillips, R. S. 12 1971 Scattering theory. Zbl 0225.35081Lax, Peter D.; Phillips, Ralph S. 11 1971 Scattering theory for the wave equation with a short range perturbation. Zbl 0465.35073Phillips, Ralph S. 10 1982 The extension of dual subspaces invariant under an algebra. Zbl 0115.33003Phillips, R. S. 10 1961 An example of Huygens’ principle. Zbl 0362.35052Lax, Peter D.; Phillips, Ralph S. 9 1978 Translation representations for automorphic solutions of the wave equation in non-Euclidean spaces. III. Zbl 0578.10033Lax, Peter D.; Phillips, Ralph S. 9 1985 Dissipative operators and parabolic partial differential equation. Zbl 0093.10002Phillips, R. S. 9 1959 A minimax characterization for the eigenvalues of a positive symmetric operator in a space with an indefinite metric. Zbl 0203.13703Phillips, R. S. 9 1970 Translation representations for automorphic solutions of the wave equation in non-Euclidean spaces. II. Zbl 0549.10019Lax, Peter D.; Phillips, Ralph S. 8 1984 Cusp forms for character varieties. Zbl 0804.11038Phillips, R.; Sarnak, P. 7 1994 The time delay operator and a related trace formula. Zbl 0463.47006Lax, Peter D.; Phillips, Ralph S. 7 1978 Automorphic spectrum and Fermi’s golden rule. Zbl 0809.30035Phillips, R.; Sarnak, P. 6 1992 Compact isospectral of plane domains. Zbl 0674.30021Osgood, B.; Phillips, R.; Sarnak, P. 6 1988 A characterization of euclidean spaces. Zbl 0024.41402Phillips, R. S. 6 1940 On Fourier-Stieltjes integrals. Zbl 0039.33101Phillips, R. S. 6 1950 Classical analysis and functional analysis: selected papers. Ed. by Robert R. Kallman. Zbl 0558.46002Hille, Einar 5 1975 Scattering theory for the wave equation with a short range perturbation. II. Zbl 0526.35066Phillips, Ralph S. 5 1984 Integration in a convex linear topological space. JFM 66.0226.01Phillips, R. S. 5 1940 On the scattering frequencies of the Laplace operator for exterior domains. Zbl 0226.35077Lax, Peter D.; Phillips, Ralph S. 5 1972 On the spectrum of the Hecke groups. Zbl 0564.30030Phillips, R. S.; Sarnak, P. 4 1985 Translation representations for the solution of the non-euclidean wave equation. II. Zbl 0446.35004Lax, Peter D.; Phillips, Ralph S. 4 1981 On the integration of the diffusion equation with boundary conditions. Zbl 0103.31501Phillips, R. S. 4 1961 A remark on the preceding paper of D. Ludwig and C.S. Morawetz. Zbl 0167.10103Phillips, R. S. 4 1969 Analytic properties of the Schrödinger scattering matrix. Zbl 0193.38302Lax, P.; Phillips, R. S. 4 1966 On the exterior problem for the reduced wave equation. Zbl 0261.35022Phillips, Ralph S. 3 1973 Translation representation for automorphic solutions of the wave equation in non-Euclidean spaces. IV. Zbl 0796.35093Lax, Peter D.; Phillips, Ralph S. 3 1992 Scattering theory for symmetric spaces of noncompact type. Zbl 0799.58081Phillips, Ralph S.; Shahshahani, Mehrdad M. 3 1993 Scattering theory for the wave equation on a hyperbolic manifold. Zbl 0657.35105Phillips, Ralph; Wiskott, Bettina; Woo, Alex 3 1987 Additive set functions and vector lattices. JFM 67.0162.02Bochner, S.; Phillips, R. S. 3 1941 A note on ergodic theory. Zbl 0043.33202Phillips, R. S. 3 1951 Semi-groups of operators. Zbl 0064.11201Phillips, R. S. 3 1955 Semi-groups of contraction operators. Zbl 0206.44402Phillips, R. S. 3 1963 A local Paley-Wiener theorem for the Radon transform of \(L_ 2\) functions in a non-Euclidean setting. Zbl 0511.58037Lax, Peter D.; Phillips, Ralph S. 2 1982 The translation representation theorem. Zbl 0481.47027Lax, Peter D.; Phillips, Ralph S. 2 1981 The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces. Zbl 0497.52007Lax, Peter D.; Phillips, Ralph S. 2 1982 Groups of positive operators. Zbl 0072.32601Dye, H. A.; Phillips, R. S. 2 1956 Energy decay for the neutrino equation in the exterior of a torus. Zbl 0225.35085Phillips, Ralph; Sarason, Leonard 2 1971 The spectrum of the Laplacian for domains in hyperbolic space and limit sets of Kleinian groups. Zbl 0559.10017Phillips, Ralph 1 1984 Perturbation theory for twisted automorphic functions. Zbl 0871.11039Phillips, R. 1 1997 Dissolving a cusp form in the presence of multiplicities. Zbl 0924.11040Judge, C. M.; Phillips, R. S. 1 1997 The circle problem in the hyperbolic plane. Zbl 0812.11035Phillips, Ralph; Rudnick, Zeév 21 1994 Cusp forms for character varieties. Zbl 0804.11038Phillips, R.; Sarnak, P. 7 1994 Scattering theory for symmetric spaces of noncompact type. Zbl 0799.58081Phillips, Ralph S.; Shahshahani, Mehrdad M. 3 1993 Perturbation theory for the Laplacian on automorphic functions. Zbl 0743.30039Phillips, R.; Sarnak, P. 22 1992 Automorphic spectrum and Fermi’s golden rule. Zbl 0809.30035Phillips, R.; Sarnak, P. 6 1992 Translation representation for automorphic solutions of the wave equation in non-Euclidean spaces. IV. Zbl 0796.35093Lax, Peter D.; Phillips, Ralph S. 3 1992 The spectrum of Fermat curves. Zbl 0751.11030Phillips, R.; Sarnak, P. 13 1991 Hodge theory on hyperbolic manifolds. Zbl 0712.58006Mazzeo, Rafe; Phillips, Ralph S. 23 1990 Scattering theory. Rev. ed. Zbl 0697.35004Lax, Peter D.; Phillips, Ralph S. 71 1989 Moduli space, heights and isospectral sets of plane domains. Zbl 0677.58045Osgood, B.; Phillips, R.; Sarnak, P. 19 1989 Ramanujan graphs. Zbl 0661.05035Lubotzky, A.; Phillips, R.; Sarnak, P. 380 1988 Extremals of determinants of Laplacians. Zbl 0653.53022Osgood, B.; Phillips, R.; Sarnak, P. 184 1988 Compact isospectral sets of surfaces. Zbl 0653.53021Osgood, B.; Phillips, R.; Sarnak, P. 56 1988 Compact isospectral of plane domains. Zbl 0674.30021Osgood, B.; Phillips, R.; Sarnak, P. 6 1988 Hecke operators and distributing points on \(S^2\). II. Zbl 0648.10034Lubotzky, A.; Phillips, R.; Sarnak, P. 41 1987 Geodesics in homology classes. Zbl 0642.53050Phillips, Ralph; Sarnak, Peter 34 1987 Scattering theory for the wave equation on a hyperbolic manifold. Zbl 0657.35105Phillips, Ralph; Wiskott, Bettina; Woo, Alex 3 1987 Hecke operators and distributing points on the sphere. I. Zbl 0619.10052Lubotzky, A.; Phillips, R.; Sarnak, P. 51 1986 On cusp forms for co-finite subgroups of PSL(2,\({\mathbb{R}})\). Zbl 0558.10017Phillips, R. S.; Sarnak, P. 71 1985 The Weyl theorem and the deformation of discrete groups. Zbl 0614.10027Phillips, R. S.; Sarnak, P. 22 1985 The Laplacian for domains in hyperbolic space and limit sets of Kleinian groups. Zbl 0611.30037Phillips, R. S.; Sarnak, P. 21 1985 Maass cusp forms. Zbl 0566.10017Deshouillers, J.-M.; Iwaniec, H.; Phillips, R. S.; Sarnak, P. 16 1985 Translation representations for automorphic solutions of the wave equation in non-Euclidean spaces. III. Zbl 0578.10033Lax, Peter D.; Phillips, Ralph S. 9 1985 On the spectrum of the Hecke groups. Zbl 0564.30030Phillips, R. S.; Sarnak, P. 4 1985 Translation representations for automorphic solutions of the wave equation in non-Euclidean spaces; the case of finite volume. Zbl 0576.30037Lax, Peter D.; Phillips, Ralph S. 1 1985 Translation representations for automorphic solutions of the wave equation in non-Euclidean spaces. I. Zbl 0544.10024Lax, Peter D.; Phillips, Ralph S. 20 1984 Translation representations for automorphic solutions of the wave equation in non-Euclidean spaces. II. Zbl 0549.10019Lax, Peter D.; Phillips, Ralph S. 8 1984 Scattering theory for the wave equation with a short range perturbation. II. Zbl 0526.35066Phillips, Ralph S. 5 1984 The spectrum of the Laplacian for domains in hyperbolic space and limit sets of Kleinian groups. Zbl 0559.10017Phillips, Ralph 1 1984 The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces. Zbl 0497.30036Lax, Peter D.; Phillips, Ralph S. 92 1982 Scattering theory for the wave equation with a short range perturbation. Zbl 0465.35073Phillips, Ralph S. 10 1982 A local Paley-Wiener theorem for the Radon transform of \(L_ 2\) functions in a non-Euclidean setting. Zbl 0511.58037Lax, Peter D.; Phillips, Ralph S. 2 1982 The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces. Zbl 0497.52007Lax, Peter D.; Phillips, Ralph S. 2 1982 Translation representations for the solution of the non-euclidean wave equation. II. Zbl 0446.35004Lax, Peter D.; Phillips, Ralph S. 4 1981 The translation representation theorem. Zbl 0481.47027Lax, Peter D.; Phillips, Ralph S. 2 1981 The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces. Zbl 0467.10037Lax, Peter D.; Phillips, Ralph S. 1 1981 Scattering theory for automorphic functions. Zbl 0442.10018Lax, Peter D.; Phillips, Ralph S. 15 1980 Translation representations for the solution of the non-Euclidean wave equation. Zbl 0425.35065Lax, Peter D.; Phillips, Ralph S. 16 1979 An example of Huygens’ principle. Zbl 0362.35052Lax, Peter D.; Phillips, Ralph S. 9 1978 The time delay operator and a related trace formula. Zbl 0463.47006Lax, Peter D.; Phillips, Ralph S. 7 1978 The scattering of sound waves by an obstacle. Zbl 0335.35075Lax, Peter D.; Phillips, Ralph S. 17 1977 Scattering theory for automorphic functions. Zbl 0362.10022Lax, Peter D.; Phillips, Ralph S. 102 1976 Classical analysis and functional analysis: selected papers. Ed. by Robert R. Kallman. Zbl 0558.46002Hille, Einar 5 1975 Functional analysis and semi-groups. 3rd printing of rev. ed. of 1957. Zbl 0392.46001Hille, Einar; Phillips, Ralph S. 66 1974 A scattering theory for automorphic functions. Zbl 0297.35061Lax, P. D.; Phillips, R. S. 12 1974 Scattering theory for dissipative hyperbolic systems. Zbl 0295.35069Lax, P. D.; Phillips, R. S. 38 1973 On the exterior problem for the reduced wave equation. Zbl 0261.35022Phillips, Ralph S. 3 1973 Scattering theory for the acoustic equation in an even number of space dimensions. Zbl 0236.35036Lax, P. D.; Phillips, R. S. 38 1972 On the scattering frequencies of the Laplace operator for exterior domains. Zbl 0226.35077Lax, Peter D.; Phillips, Ralph S. 5 1972 A logarithmic bound on the location of the poles of the scattering matrix. Zbl 0216.13002Lax, P. D.; Phillips, R. S. 15 1971 Scattering theory. (Teoriya rasseyaniya). Zbl 0212.43802Lax, P. D.; Phillips, R. S. 12 1971 Scattering theory. Zbl 0225.35081Lax, Peter D.; Phillips, Ralph S. 11 1971 Energy decay for the neutrino equation in the exterior of a torus. Zbl 0225.35085Phillips, Ralph; Sarason, Leonard 2 1971 The Paley-Wiener theorem for the Radon transform. Zbl 0189.14803Lax, Peter D.; Phillips, R. S. 19 1970 A minimax characterization for the eigenvalues of a positive symmetric operator in a space with an indefinite metric. Zbl 0203.13703Phillips, R. S. 9 1970 Decaying modes for the wave equation in the exterior of an obstacle. Zbl 0181.38201Lax, Peter D.; Phillips, R. S. 33 1969 On dissipative operators. Zbl 0181.15301Phillips, R. S. 12 1969 A remark on the preceding paper of D. Ludwig and C.S. Morawetz. Zbl 0167.10103Phillips, R. S. 4 1969 Elliptic-parabolic equations of the second order. Zbl 0163.34402Phillips, R. S.; Sarason, L. 23 1968 On symplectic mappings of contraction operators. Zbl 0167.13501Phillips, R. S. 15 1968 On the extension problem for dissipative operators. Zbl 0167.13404Crandall, M. G.; Phillips, R. S. 14 1968 Scattering theory for transport phenomena. Zbl 0214.12002Lax, P. D.; Phillips, R. S. 211 1967 Scattering theory. Zbl 0186.16301Lax, Peter D.; Phillips, Ralph S. 108 1967 The acoustic equation with an indefinite energy form and the Schrödinger equation. Zbl 0186.16401Lax, P. D.; Phillips, R. S. 12 1967 On matrices whose real linear combinations are nonsingular. Zbl 0168.02404Adams, J. F.; Lax, P. D.; Phillips, R. S. 39 1966 Singular symmetric positive first order differential operators. Zbl 0141.28701Phillips, R. S.; Sarason, L. 19 1966 Analytic properties of the Schrödinger scattering matrix. Zbl 0193.38302Lax, P.; Phillips, R. S. 4 1966 The translation representation of the solution of the wave equation in free spaces. Zbl 0184.13202Lax, P. D.; Phillips, R. S. 1 1966 Dissipative ordinary differential operators. Zbl 0135.14602Olubummo, A.; Phillips, R. S. 1 1965 Scattering theory. Zbl 0117.09104Lax, P. D.; Phillips, R. S. 56 1964 Exponential decay of solutions of the wave equation in the exterior of a star-shaped obstacle. Zbl 0161.08001Lax, Peter D.; Morawetz, C. S.; Phillips, R. S. 49 1963 Semi-groups of contraction operators. Zbl 0206.44402Phillips, R. S. 3 1963 Semi-groups of positive contraction operators. Zbl 0113.09901Phillips, R. S. 19 1962 The wave equation in exterior domains. Zbl 0103.06401Lax, Peter D.; Phillips, Ralph S. 14 1962 The exponential decay of solutions of the wave equation in the exterior of a star-shaped obstacle. Zbl 0108.28301Lax, P. D.; Morawetz, C. S.; Phillips, R. S. 12 1962 Dissipative operators in a Banach space. Zbl 0101.09503Lumer, G.; Phillips, R. S. 148 1961 The extension of dual subspaces invariant under an algebra. Zbl 0115.33003Phillips, R. S. 10 1961 On the integration of the diffusion equation with boundary conditions. Zbl 0103.31501Phillips, R. S. 4 1961 Local boundary conditions for dissipative symmetric linear differential operators. Zbl 0094.07502Lax, Peter; Phillips, R. S. 176 1960 Dissipative operators and hyperbolic systems of partial differential equation. Zbl 0093.10001Phillips, R. S. 114 1959 Dissipative operators and parabolic partial differential equation. Zbl 0093.10002Phillips, R. S. 9 1959 On a theorem due to Sz.-Nagy. Zbl 0085.32703Phillips, R. S. 1 1959 Functional analysis and semigroups. Rev. ed. Zbl 0078.10004Hille, Einar; Phillips, Ralph S. 1,388 1957 Dissipative hyperbolic systems. Zbl 0081.31102Phillips, R. S. 15 1957 Groups of positive operators. Zbl 0072.32601Dye, H. A.; Phillips, R. S. 2 1956 The adjoint semi-group. Zbl 0064.11202Phillips, R. S. 39 1955 Semi-groups of operators. Zbl 0064.11201Phillips, R. S. 3 1955 An inversion formula for Laplace transforms and semi-groups of linear operators. Zbl 0059.10704Phillips, R. S. 69 1954 A note on the abstract Cauchy problem. Zbl 0058.10603Phillips, R. S. 16 1954 Perturbation theory for semi-groups of linear operators. Zbl 0053.08704Phillips, R. S. 62 1953 On the generation of semigroups of linear operators. Zbl 0047.11004Phillips, R. S. 53 1952 On one-parameter semi-groups of linear transformations. Zbl 0043.11404Phillips, R. S. 14 1951 Spectral theory for semi-groups of linear operators. Zbl 0045.21502Phillips, R. S. 14 1951 A note on ergodic theory. Zbl 0043.33202Phillips, R. S. 3 1951 Bessel function approximations. Zbl 0036.04001Phillips, R. S.; Malin, Henry 18 1950 On Fourier-Stieltjes integrals. Zbl 0039.33101Phillips, R. S. 6 1950 On weakly compact subsets of a Banach space. Zbl 0063.06212Phillips, R. S. 53 1943 Absolutely convergent Fourier expansions for non-commutative normed rings. Zbl 0060.27204Bochner, Salomon; Phillips, R. S. 42 1942 ...and 8 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 3,925 Authors 38 Phillips, Ralph Saul 32 Jørgensen, Palle E. T. 31 Sarnak, Peter Clive 21 Gupta, Vijay 21 Petkov, Vesselin M. 20 Goldstein, Jerome Arthur 18 Rauch, Jeffrey B. 17 Baskakov, Anatoliĭ Grigor’evich 17 Miyadera, Isao 15 Butzer, Paul Leo 14 Allahverdiev, Bilender Paşaoğlu 14 Alon, Noga M. 14 Lasiecka, Irena 14 Lax, Peter David 14 Sgibnev, Mikhaĭl Sergeevich 13 Da Prato, Giuseppe 12 Perla Menzala, Gustavo Alberto 12 Stoyanov, Luchezar N. 11 Branson, Thomas Patrick 11 Zworski, Maciej 10 Batty, Charles J. K. 10 Bourgain, Jean 10 Choi, Junesang 10 Jorgenson, Jay Alan 10 Kontorovich, Alex V. 10 Lubotzky, Alexander 10 Oh, Hee 10 Perry, Peter A. 10 Strauss, Walter Alexander 10 Wilcox, Calvin H. 9 Kantorovitz, Shmuel 9 Linial, Nathan 9 Petridis, Yiannis N. 9 Ricker, Werner Joseph 9 Risager, Morten S. 9 Sá Barreto, Antônio 9 Schulenberger, John R. 9 Triggiani, Roberto 9 van Neerven, Jan M. A. M. 8 Arendt, Wolfgang 8 Bardos, Claude Williams 8 Bäumer, Boris 8 Brooks, James K. 8 Gamburd, Alexander 8 Kato, Tosio 8 Korotkov, Vitalii Borisovich 8 Oharu, Shinnosuke 8 Sharp, Richard W. 8 Shaw, Sen-Yen 8 Taylor, Michael Eugene 8 Uhl, J. Jerry jun. 7 Alpay, Daniel Aron 7 Bakaev, Nikolai Yu. 7 Ball, Joseph Anthony 7 Bobrowski, Adam 7 Bratteli, Ola 7 Chang, Sun-Yung Alice 7 Gohberg, Israel 7 Gustafson, Karl Edwin 7 Judge, Christopher M. 7 Kaashoek, Marinus Adriaan 7 Meerschaert, Mark Marvin 7 Mirotin, Adol’f Rubimovich 7 Naud, Frédéric 7 Parzanchevski, Ori 7 Popivanov, Nedyu Iv. 7 Prüß, Jan Wilhelm 7 Soga, Hideo 7 Sogge, Christopher D. 7 Strichartz, Robert S. 7 Tachev, Gancho T. 7 Terras, Audrey Anne 7 Trakhinin, Yuri L. 7 Zaidman, Samuel D. 7 Zelditch, Steve 6 Anantharaman, Nalini 6 Antoniou, Ioannis E. 6 Awonusika, Richard Olu 6 Baricz, Árpád 6 Berens, Hubert Anton 6 Bétermin, Laurent 6 Browder, Felix Earl 6 Chernoff, Paul R. 6 Christiansen, Tanya J. 6 Cooper, Jeffery M. 6 Davies, Edward Brian 6 Dinculeanu, Nicolae 6 Dobrakov, Ivan 6 Epstein, Charles Lawrence 6 Fan, Ky 6 Fattorini, Hector O. 6 Garofalo, Nicola 6 Gomilko, Alexandre M. 6 Görlich, Ernst 6 Helton, John William 6 Lapidus, Michel L. 6 Lazebnik, Felix 6 Liu, Hongyu 6 Metcalfe, Jason L. 6 Mohar, Bojan ...and 3,825 more Authors all top 5 Cited in 528 Serials 193 Transactions of the American Mathematical Society 190 Proceedings of the American Mathematical Society 189 Journal of Mathematical Analysis and Applications 169 Journal of Functional Analysis 99 Mathematische Annalen 93 Communications in Mathematical Physics 81 Journal of Differential Equations 69 Mathematische Zeitschrift 66 Archive for Rational Mechanics and Analysis 63 Duke Mathematical Journal 63 Bulletin of the American Mathematical Society 56 Siberian Mathematical Journal 54 Semigroup Forum 51 Integral Equations and Operator Theory 46 Advances in Mathematics 41 Israel Journal of Mathematics 41 Annales de l’Institut Fourier 40 Mathematical Notes 40 Ukrainian Mathematical Journal 40 Communications in Partial Differential Equations 37 Linear Algebra and its Applications 34 Archiv der Mathematik 34 Tohoku Mathematical Journal. Second Series 32 Journal of Mathematical Physics 31 Publications of the Research Institute for Mathematical Sciences, Kyoto University 30 Annali di Matematica Pura ed Applicata. Serie Quarta 29 Journal d’Analyse Mathématique 28 Functional Analysis and its Applications 28 Journal of Mathematical Sciences (New York) 27 Rendiconti del Seminario Matematico della Università di Padova 26 Proceedings of the Japan Academy 24 Inventiones Mathematicae 24 Bulletin of the American Mathematical Society. New Series 22 Acta Mathematica 22 Combinatorica 20 Results in Mathematics 20 Geometric and Functional Analysis. GAFA 19 Computers & Mathematics with Applications 19 Journal of Soviet Mathematics 19 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 19 Journal of Evolution Equations 19 Complex Analysis and Operator Theory 18 Applied Mathematics and Optimization 18 Journal of Combinatorial Theory. Series B 17 The Journal of Geometric Analysis 17 Nonlinear Analysis. Theory, Methods & Applications 16 Journal of Number Theory 15 Mathematical Methods in the Applied Sciences 15 Annales de l’Institut Henri Poincaré. Physique Théorique 15 Annali della Scuola Normale Superiore di Pisa. Scienze Fisiche e Matematiche. III. Ser 14 Discrete Mathematics 14 Journal of Statistical Physics 14 Rocky Mountain Journal of Mathematics 14 Czechoslovak Mathematical Journal 14 Mathematische Nachrichten 14 Acta Applicandae Mathematicae 13 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 13 Applied Mathematics and Computation 13 Monatshefte für Mathematik 13 Proceedings of the Japan Academy. Series A 13 Theoretical Computer Science 13 European Journal of Combinatorics 13 Systems & Control Letters 12 Mathematics of Computation 12 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 12 Numerische Mathematik 11 Bulletin of the Australian Mathematical Society 11 Communications on Pure and Applied Mathematics 11 International Journal of Theoretical Physics 11 Mathematical Proceedings of the Cambridge Philosophical Society 11 Compositio Mathematica 11 Manuscripta Mathematica 11 Probability Theory and Related Fields 11 SIAM Journal on Mathematical Analysis 11 Indagationes Mathematicae. New Series 11 Potential Analysis 10 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 10 Journal of Computational and Applied Mathematics 10 Mathematical Systems Theory 10 Journal of the American Mathematical Society 10 Aequationes Mathematicae 10 Russian Mathematics 10 Abstract and Applied Analysis 10 Differential Equations 10 Journal of Hyperbolic Differential Equations 10 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 9 Applicable Analysis 9 Letters in Mathematical Physics 9 Journal of Approximation Theory 9 Rendiconti del Circolo Matemàtico di Palermo. Serie II 9 Ergodic Theory and Dynamical Systems 9 Combinatorics, Probability and Computing 9 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 9 Mediterranean Journal of Mathematics 8 Discrete Applied Mathematics 8 Lithuanian Mathematical Journal 8 Reports on Mathematical Physics 8 Theoretical and Mathematical Physics 8 Arkiv för Matematik 8 Chaos, Solitons and Fractals ...and 428 more Serials all top 5 Cited in 61 Fields 1,111 Operator theory (47-XX) 1,005 Partial differential equations (35-XX) 517 Functional analysis (46-XX) 353 Global analysis, analysis on manifolds (58-XX) 295 Ordinary differential equations (34-XX) 283 Combinatorics (05-XX) 281 Number theory (11-XX) 265 Probability theory and stochastic processes (60-XX) 216 Quantum theory (81-XX) 155 Differential geometry (53-XX) 141 Functions of a complex variable (30-XX) 132 Measure and integration (28-XX) 128 Numerical analysis (65-XX) 126 Dynamical systems and ergodic theory (37-XX) 124 Fluid mechanics (76-XX) 118 Topological groups, Lie groups (22-XX) 115 Systems theory; control (93-XX) 106 Computer science (68-XX) 97 Approximations and expansions (41-XX) 92 Integral equations (45-XX) 91 Abstract harmonic analysis (43-XX) 85 Real functions (26-XX) 83 Statistical mechanics, structure of matter (82-XX) 70 Group theory and generalizations (20-XX) 70 Harmonic analysis on Euclidean spaces (42-XX) 63 Several complex variables and analytic spaces (32-XX) 60 Mechanics of deformable solids (74-XX) 59 Linear and multilinear algebra; matrix theory (15-XX) 58 Special functions (33-XX) 52 Optics, electromagnetic theory (78-XX) 48 Calculus of variations and optimal control; optimization (49-XX) 42 Difference and functional equations (39-XX) 40 Information and communication theory, circuits (94-XX) 39 Relativity and gravitational theory (83-XX) 34 Potential theory (31-XX) 34 Integral transforms, operational calculus (44-XX) 33 Biology and other natural sciences (92-XX) 32 Manifolds and cell complexes (57-XX) 32 Operations research, mathematical programming (90-XX) 30 Algebraic geometry (14-XX) 30 Convex and discrete geometry (52-XX) 29 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 28 General topology (54-XX) 19 Mathematical logic and foundations (03-XX) 19 Statistics (62-XX) 14 Geometry (51-XX) 14 Mechanics of particles and systems (70-XX) 13 Sequences, series, summability (40-XX) 10 Order, lattices, ordered algebraic structures (06-XX) 10 Algebraic topology (55-XX) 9 History and biography (01-XX) 8 Nonassociative rings and algebras (17-XX) 7 Associative rings and algebras (16-XX) 6 Geophysics (86-XX) 5 General and overarching topics; collections (00-XX) 4 Field theory and polynomials (12-XX) 4 Category theory; homological algebra (18-XX) 4 \(K\)-theory (19-XX) 4 Astronomy and astrophysics (85-XX) 1 Commutative algebra (13-XX) 1 Classical thermodynamics, heat transfer (80-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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