Edit Profile Phillips, Ralph Saul Compute Distance To: Compute Author ID: phillips.ralph-saul Published as: Phillips, R.; Phillips, R. S.; Phillips, Ralph; Phillips, Ralph S. External Links: MGP · Wikidata · GND Documents Indexed: 124 Publications since 1940, including 6 Books Biographic References: 1 Publication all top 5 Co-Authors 44 single-authored 45 Lax, Peter David 17 Sarnak, Peter Clive 4 Osgood, Brad G. 3 Lubotzky, Alexander 3 Sarason, Leonard 2 Bochner, Salomon 2 Hille, Einar 2 Synge Morawetz, Cathleen 2 Wiskott, Bettina 2 Woo, Alex C. 1 Adams, John Frank 1 Crandall, Michael G. 1 Deshouillers, Jean-Marc 1 Dye, Henry Abel 1 Iwaniec, Henryk 1 Judge, Christopher M. 1 Lumer, Gunter 1 Malin, Henry 1 Mazzeo, Rafe R. 1 Olubummo, Adegoke 1 Rudnick, Zeév 1 Shahshahani, Mehrdad M. all top 5 Serials 19 Communications on Pure and Applied Mathematics 10 Transactions of the American Mathematical Society 8 Journal of Functional Analysis 8 Bulletin of the American Mathematical Society 5 Duke Mathematical Journal 4 Pacific Journal of Mathematics 4 Annals of Mathematics. Second Series 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 all top 5 Fields 46 Partial differential equations (35-XX) 32 Number theory (11-XX) 20 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) 3 Measure and integration (28-XX) 3 Integral transforms, operational calculus (44-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Geometry (51-XX) 2 Quantum theory (81-XX) 1 History and biography (01-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 Functional analysis (46-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 104 Publications have been cited 4,920 times in 4,198 Documents Cited by ▼ Year ▼ Functional analysis and semigroups. Rev. ed. Zbl 0078.10004Hille, Einar; Phillips, Ralph S. 1,784 1957 Ramanujan graphs. Zbl 0661.05035Lubotzky, A.; Phillips, R.; Sarnak, P. 344 1988 Scattering theory for transport phenomena. Zbl 0214.12002Lax, P. D.; Phillips, R. S. 220 1967 Extremals of determinants of Laplacians. Zbl 0653.53022Osgood, B.; Phillips, R.; Sarnak, P. 165 1988 Local boundary conditions for dissipative symmetric linear differential operators. Zbl 0094.07502Lax, Peter; Phillips, R. S. 159 1960 Dissipative operators in a Banach space. Zbl 0101.09503Lumer, G.; Phillips, R. S. 144 1961 Scattering theory. Zbl 0186.16301Lax, Peter D.; Phillips, Ralph S. 115 1967 Scattering theory for automorphic functions. Zbl 0362.10022Lax, Peter D.; Phillips, Ralph S. 109 1976 Dissipative operators and hyperbolic systems of partial differential equation. Zbl 0093.10001Phillips, R. S. 109 1959 The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces. Zbl 0497.30036Lax, Peter D.; Phillips, Ralph S. 89 1982 Functional analysis and semi-groups. 3rd printing of rev. ed. of 1957. Zbl 0392.46001Hille, Einar; Phillips, Ralph S. 80 1974 Scattering theory. Rev. ed. Zbl 0697.35004Lax, Peter D.; Phillips, Ralph S. 79 1989 On linear transformations. Zbl 0025.34202Phillips, R. S. 78 1940 On cusp forms for co-finite subgroups of PSL(2,\({\mathbb{R}})\). Zbl 0558.10017Phillips, R. S.; Sarnak, P. 67 1985 An inversion formula for Laplace transforms and semi-groups of linear operators. Zbl 0059.10704Phillips, R. S. 60 1954 Scattering theory. Zbl 0117.09104Lax, P. D.; Phillips, R. S. 57 1964 Compact isospectral sets of surfaces. Zbl 0653.53021Osgood, B.; Phillips, R.; Sarnak, P. 52 1988 On weakly compact subsets of a Banach space. Zbl 0063.06212Phillips, R. S. 51 1943 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 On the generation of semigroups of linear operators. Zbl 0047.11004Phillips, R. S. 49 1952 Hecke operators and distributing points on the sphere. I. Zbl 0619.10052Lubotzky, A.; Phillips, R.; Sarnak, P. 46 1986 Absolutely convergent Fourier expansions for non-commutative normed rings. Zbl 0060.27204Bochner, Salomon; Phillips, R. S. 41 1942 Scattering theory for the acoustic equation in an even number of space dimensions. Zbl 0236.35036Lax, P. D.; Phillips, R. S. 38 1972 The adjoint semi-group. Zbl 0064.11202Phillips, R. S. 38 1955 Scattering theory for dissipative hyperbolic systems. Zbl 0295.35069Lax, P. D.; Phillips, R. S. 37 1973 Hecke operators and distributing points on \(S^2\). II. Zbl 0648.10034Lubotzky, A.; Phillips, R.; Sarnak, P. 36 1987 On matrices whose real linear combinations are nonsingular. Zbl 0168.02404Adams, J. F.; Lax, P. D.; Phillips, R. S. 36 1966 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. 27 1940 Hodge theory on hyperbolic manifolds. Zbl 0712.58006Mazzeo, Rafe; Phillips, Ralph S. 24 1990 Elliptic-parabolic equations of the second order. Zbl 0163.34402Phillips, R. S.; Sarason, L. 23 1968 The Weyl theorem and the deformation of discrete groups. Zbl 0614.10027Phillips, R. S.; Sarnak, P. 21 1985 The Laplacian for domains in hyperbolic space and limit sets of Kleinian groups. Zbl 0611.30037Phillips, R. S.; Sarnak, P. 20 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 Additive set functions and vector lattices. Zbl 0026.00105Bochner, Salomon; Phillips, R. S. 19 1941 The circle problem in the hyperbolic plane. Zbl 0812.11035Phillips, Ralph; Rudnick, Zeév 18 1994 Perturbation theory for the Laplacian on automorphic functions. Zbl 0743.30039Phillips, R.; Sarnak, P. 18 1992 The scattering of sound waves by an obstacle. Zbl 0335.35075Lax, Peter D.; Phillips, Ralph S. 18 1977 Singular symmetric positive first order differential operators. Zbl 0141.28701Phillips, R. S.; Sarason, L. 18 1966 Semi-groups of positive contraction operators. Zbl 0113.09901Phillips, R. S. 18 1962 Moduli space, heights and isospectral sets of plane domains. Zbl 0677.58045Osgood, B.; Phillips, R.; Sarnak, P. 17 1989 The Paley-Wiener theorem for the Radon transform. Zbl 0189.14803Lax, Peter D.; Phillips, R. S. 17 1970 Translation representations for the solution of the non-Euclidean wave equation. Zbl 0425.35065Lax, Peter D.; Phillips, Ralph S. 16 1979 Bessel function approximations. Zbl 0036.04001Phillips, R. S.; Malin, Henry 16 1950 Maass cusp forms. Zbl 0566.10017Deshouillers, J.-M.; Iwaniec, H.; Phillips, R. S.; Sarnak, P. 15 1985 A logarithmic bound on the location of the poles of the scattering matrix. Zbl 0216.13002Lax, P. D.; Phillips, R. S. 15 1971 On symplectic mappings of contraction operators. Zbl 0167.13501Phillips, R. S. 15 1968 The extension of dual subspaces invariant under an algebra. Zbl 0115.33003Phillips, R. S. 15 1961 Scattering theory. Zbl 0225.35081Lax, Peter D.; Phillips, Ralph S. 14 1971 The wave equation in exterior domains. Zbl 0103.06401Lax, Peter D.; Phillips, Ralph S. 14 1962 A note on the abstract Cauchy problem. Zbl 0058.10603Phillips, R. S. 14 1954 Spectral theory for semi-groups of linear operators. Zbl 0045.21502Phillips, R. S. 14 1951 On one-parameter semi-groups of linear transformations. Zbl 0043.11404Phillips, R. S. 14 1951 The spectrum of Fermat curves. Zbl 0751.11030Phillips, R.; Sarnak, P. 13 1991 Scattering theory for automorphic functions. Zbl 0442.10018Lax, Peter D.; Phillips, Ralph S. 13 1980 A scattering theory for automorphic functions. Zbl 0297.35061Lax, P. D.; Phillips, R. S. 13 1974 On the extension problem for dissipative operators. Zbl 0167.13404Crandall, M. G.; Phillips, R. S. 13 1968 Scattering theory. (Teoriya rasseyaniya). Zbl 0212.43802Lax, P. D.; Phillips, R. S. 12 1971 The acoustic equation with an indefinite energy form and the Schrödinger equation. Zbl 0186.16401Lax, P. D.; Phillips, R. S. 12 1967 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 linear transformations. JFM 66.0554.01Phillips, R. S. 12 1940 Translation representations for automorphic solutions of the wave equation in non-Euclidean spaces. III. Zbl 0578.10033Lax, Peter D.; Phillips, Ralph S. 11 1985 An example of Huygens’ principle. Zbl 0362.35052Lax, Peter D.; Phillips, Ralph S. 11 1978 On dissipative operators. Zbl 0181.15301Phillips, R. S. 11 1969 Scattering theory for the wave equation with a short range perturbation. Zbl 0465.35073Phillips, Ralph S. 10 1982 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 Dissipative operators and parabolic partial differential equation. Zbl 0093.10002Phillips, R. S. 9 1959 On the scattering frequencies of the Laplace operator for exterior domains. Zbl 0226.35077Lax, Peter D.; Phillips, Ralph S. 8 1972 Cusp forms for character varieties. Zbl 0804.11038Phillips, R.; Sarnak, P. 7 1994 Translation representations for automorphic solutions of the wave equation in non-Euclidean spaces. II. Zbl 0549.10019Lax, Peter D.; Phillips, Ralph S. 7 1984 Automorphic spectrum and Fermi’s golden rule. Zbl 0809.30035Phillips, R.; Sarnak, P. 6 1992 The time delay operator and a related trace formula. Zbl 0463.47006Lax, Peter D.; Phillips, Ralph S. 6 1978 Analytic properties of the Schrödinger scattering matrix. Zbl 0193.38302Lax, P.; Phillips, R. S. 6 1966 A characterization of euclidean spaces. Zbl 0024.41402Phillips, R. S. 6 1940 Scattering theory for the wave equation with a short range perturbation. II. Zbl 0526.35066Phillips, Ralph S. 5 1984 On Fourier-Stieltjes integrals. Zbl 0039.33101Phillips, R. S. 5 1950 Integration in a convex linear topological space. JFM 66.0226.01Phillips, R. S. 5 1940 Compact isospectral of plane domains. Zbl 0674.30021Osgood, B.; Phillips, R.; Sarnak, P. 4 1988 Translation representations for the solution of the non-euclidean wave equation. II. Zbl 0446.35004Lax, Peter D.; Phillips, Ralph S. 4 1981 On the exterior problem for the reduced wave equation. Zbl 0261.35022Phillips, Ralph S. 4 1973 A remark on the preceding paper of D. Ludwig and C.S. Morawetz. Zbl 0167.10103Phillips, R. S. 4 1969 On the integration of the diffusion equation with boundary conditions. Zbl 0103.31501Phillips, R. S. 4 1961 Scattering theory for symmetric spaces of noncompact type. Zbl 0799.58081Phillips, Ralph S.; Shahshahani, Mehrdad M. 3 1993 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 the wave equation on a hyperbolic manifold. Zbl 0657.35105Phillips, Ralph; Wiskott, Bettina; Woo, Alex 3 1987 On the spectrum of the Hecke groups. Zbl 0564.30030Phillips, R. S.; Sarnak, P. 3 1985 Semi-groups of contraction operators. Zbl 0206.44402Phillips, R. S. 3 1963 Semi-groups of operators. Zbl 0064.11201Phillips, R. S. 3 1955 A note on ergodic theory. Zbl 0043.33202Phillips, R. S. 3 1951 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 Energy decay for the neutrino equation in the exterior of a torus. Zbl 0225.35085Phillips, Ralph; Sarason, Leonard 2 1971 Groups of positive operators. Zbl 0072.32601Dye, H. A.; Phillips, R. S. 2 1956 Dissolving a cusp form in the presence of multiplicities. Zbl 0924.11040Judge, C. M.; Phillips, R. S. 1 1997 Perturbation theory for twisted automorphic functions. Zbl 0871.11039Phillips, R. 1 1997 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 The spectrum of the Laplacian for domains in hyperbolic space and limit sets of Kleinian groups. Zbl 0559.10017Phillips, Ralph 1 1984 The translation representation theorem. Zbl 0481.47027Lax, Peter D.; Phillips, Ralph S. 1 1981 The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces. Zbl 0467.10037Lax, Peter D.; Phillips, Ralph S. 1 1981 Dissolving a cusp form in the presence of multiplicities. Zbl 0924.11040Judge, C. M.; Phillips, R. S. 1 1997 Perturbation theory for twisted automorphic functions. Zbl 0871.11039Phillips, R. 1 1997 The circle problem in the hyperbolic plane. Zbl 0812.11035Phillips, Ralph; Rudnick, Zeév 18 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. 18 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. 24 1990 Scattering theory. Rev. ed. Zbl 0697.35004Lax, Peter D.; Phillips, Ralph S. 79 1989 Moduli space, heights and isospectral sets of plane domains. Zbl 0677.58045Osgood, B.; Phillips, R.; Sarnak, P. 17 1989 Ramanujan graphs. Zbl 0661.05035Lubotzky, A.; Phillips, R.; Sarnak, P. 344 1988 Extremals of determinants of Laplacians. Zbl 0653.53022Osgood, B.; Phillips, R.; Sarnak, P. 165 1988 Compact isospectral sets of surfaces. Zbl 0653.53021Osgood, B.; Phillips, R.; Sarnak, P. 52 1988 Compact isospectral of plane domains. Zbl 0674.30021Osgood, B.; Phillips, R.; Sarnak, P. 4 1988 Hecke operators and distributing points on \(S^2\). II. Zbl 0648.10034Lubotzky, A.; Phillips, R.; Sarnak, P. 36 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. 46 1986 On cusp forms for co-finite subgroups of PSL(2,\({\mathbb{R}})\). Zbl 0558.10017Phillips, R. S.; Sarnak, P. 67 1985 The Weyl theorem and the deformation of discrete groups. Zbl 0614.10027Phillips, R. S.; Sarnak, P. 21 1985 The Laplacian for domains in hyperbolic space and limit sets of Kleinian groups. Zbl 0611.30037Phillips, R. S.; Sarnak, P. 20 1985 Maass cusp forms. Zbl 0566.10017Deshouillers, J.-M.; Iwaniec, H.; Phillips, R. S.; Sarnak, P. 15 1985 Translation representations for automorphic solutions of the wave equation in non-Euclidean spaces. III. Zbl 0578.10033Lax, Peter D.; Phillips, Ralph S. 11 1985 On the spectrum of the Hecke groups. Zbl 0564.30030Phillips, R. S.; Sarnak, P. 3 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. 7 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. 89 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. 1 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. 13 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. 11 1978 The time delay operator and a related trace formula. Zbl 0463.47006Lax, Peter D.; Phillips, Ralph S. 6 1978 The scattering of sound waves by an obstacle. Zbl 0335.35075Lax, Peter D.; Phillips, Ralph S. 18 1977 Scattering theory for automorphic functions. Zbl 0362.10022Lax, Peter D.; Phillips, Ralph S. 109 1976 Functional analysis and semi-groups. 3rd printing of rev. ed. of 1957. Zbl 0392.46001Hille, Einar; Phillips, Ralph S. 80 1974 A scattering theory for automorphic functions. Zbl 0297.35061Lax, P. D.; Phillips, R. S. 13 1974 Scattering theory for dissipative hyperbolic systems. Zbl 0295.35069Lax, P. D.; Phillips, R. S. 37 1973 On the exterior problem for the reduced wave equation. Zbl 0261.35022Phillips, Ralph S. 4 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. 8 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. Zbl 0225.35081Lax, Peter D.; Phillips, Ralph S. 14 1971 Scattering theory. (Teoriya rasseyaniya). Zbl 0212.43802Lax, P. D.; Phillips, R. S. 12 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. 17 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. 11 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. 13 1968 Scattering theory for transport phenomena. Zbl 0214.12002Lax, P. D.; Phillips, R. S. 220 1967 Scattering theory. Zbl 0186.16301Lax, Peter D.; Phillips, Ralph S. 115 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. 36 1966 Singular symmetric positive first order differential operators. Zbl 0141.28701Phillips, R. S.; Sarason, L. 18 1966 Analytic properties of the Schrödinger scattering matrix. Zbl 0193.38302Lax, P.; Phillips, R. S. 6 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. 57 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. 18 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. 144 1961 The extension of dual subspaces invariant under an algebra. Zbl 0115.33003Phillips, R. S. 15 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. 159 1960 Dissipative operators and hyperbolic systems of partial differential equation. Zbl 0093.10001Phillips, R. S. 109 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. 1,784 1957 Groups of positive operators. Zbl 0072.32601Dye, H. A.; Phillips, R. S. 2 1956 The adjoint semi-group. Zbl 0064.11202Phillips, R. S. 38 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. 60 1954 A note on the abstract Cauchy problem. Zbl 0058.10603Phillips, R. S. 14 1954 On the generation of semigroups of linear operators. Zbl 0047.11004Phillips, R. S. 49 1952 Spectral theory for semi-groups of linear operators. Zbl 0045.21502Phillips, R. S. 14 1951 On one-parameter semi-groups of linear transformations. Zbl 0043.11404Phillips, 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 16 1950 On Fourier-Stieltjes integrals. Zbl 0039.33101Phillips, R. S. 5 1950 On weakly compact subsets of a Banach space. Zbl 0063.06212Phillips, R. S. 51 1943 Absolutely convergent Fourier expansions for non-commutative normed rings. Zbl 0060.27204Bochner, Salomon; Phillips, R. S. 41 1942 Additive set functions and vector lattices. Zbl 0026.00105Bochner, Salomon; Phillips, R. S. 19 1941 On linear transformations. Zbl 0025.34202Phillips, R. S. 78 1940 Integration in a convex linear topological space. Zbl 0022.31902Phillips, R. S. 27 1940 ...and 4 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 4,085 Authors 37 Phillips, Ralph Saul 33 Jørgensen, Palle E. T. 31 Sarnak, Peter Clive 21 Gupta, Vijay 19 Goldstein, Jerome Arthur 18 Petkov, Vesselin M. 17 Baskakov, Anatoliĭ Grigor’evich 17 Butzer, Paul Leo 17 Rauch, Jeffrey B. 16 Lasiecka, Irena 15 Miyadera, Isao 14 Allahverdiev, Bilender Paşaoğlu 14 Lax, Peter David 13 Alon, Noga M. 13 Da Prato, Giuseppe 13 Sgibnev, Mikhaĭl Sergeevich 13 Triggiani, Roberto 12 Branson, Thomas Patrick 12 Kantorovitz, Shmuel 12 Perla Menzala, Gustavo Alberto 12 Stoyanov, Luchezar N. 12 Zworski, Maciej 11 Batty, Charles J. K. 11 Bobrowski, Adam 11 Shaw, Sen-Yen 11 van Neerven, Jan M. A. M. 10 Arendt, Wolfgang 10 Bourgain, Jean 10 Choi, Junesang 10 Kontorovich, Alex V. 10 Perry, Peter A. 10 Strauss, Walter Alexander 10 Wilcox, Calvin H. 9 Meerschaert, Mark M. 9 Oh, Hee 9 Ricker, Werner Joseph 9 Sá Barreto, Antônio 9 Salem, Hussein A. H. 9 Schulenberger, John R. 8 Alpay, Daniel Aron 8 Amann, Herbert 8 Bardos, Claude Williams 8 Bäumer, Boris 8 Brooks, James K. 8 Gamburd, Alexander 8 Harris, Lawrence A. 8 Jorgenson, Jay Alan 8 Kato, Tosio 8 Korotkov, Vitalii Borisovich 8 Linial, Nathan 8 Lubotzky, Alexander 8 Masani, Pesi Rustom 8 Reich, Simeon 8 Sharp, Richard W. 8 Sogge, Christopher D. 8 Stefanov, Plamen D. 8 Taylor, Michael Eugene 8 Tomilov, Yuri 8 Uhl, J. Jerry jun. 8 Webb, Glenn Francis 7 Bakaev, Nikolai Yu. 7 Ball, Joseph Anthony 7 Bratteli, Ola 7 Chang, Sun-Yung Alice 7 Chernoff, Paul R. 7 Christiansen, Tanya J. 7 Davies, Edward Brian 7 Gohberg, Israel 7 Gomilko, Alexandre M. 7 Jefferies, Brian R. F. 7 Judge, Christopher M. 7 Kaashoek, Marinus Adriaan 7 Metcalfe, Jason L. 7 Mirotin, Adol’f Rubimovich 7 Naud, Frédéric 7 Petridis, Yiannis N. 7 Prüß, Jan Wilhelm 7 Risager, Morten S. 7 Soga, Hideo 7 Strichartz, Robert S. 7 Tachev, Gancho T. 7 Terras, Audrey Anne 7 Zaidman, Samuel D. 7 Zelditch, Steve 6 Alzer, Horst 6 Antoniou, Ioannis E. 6 Awonusika, Richard Olu 6 Baricz, Árpád 6 Berens, Hubert Anton 6 Bingham, Nicholas Hugh 6 Brézis, Haïm 6 Browder, Felix Earl 6 Cooper, Jeffery M. 6 Curtain, Ruth Frances 6 Dinculeanu, Nicolae 6 Dobrakov, Ivan 6 ElMennaoui, Omar 6 Fan, Ky 6 Fattorini, Hector O. 6 Friedman, Avner ...and 3,985 more Authors all top 5 Cited in 492 Serials 319 Journal of Mathematical Analysis and Applications 241 Journal of Functional Analysis 191 Transactions of the American Mathematical Society 187 Proceedings of the American Mathematical Society 117 Journal of Differential Equations 98 Mathematische Annalen 90 Communications in Mathematical Physics 67 Mathematische Zeitschrift 64 Archive for Rational Mechanics and Analysis 63 Bulletin of the American Mathematical Society 60 Duke Mathematical Journal 54 Siberian Mathematical Journal 53 Advances in Mathematics 51 Integral Equations and Operator Theory 51 Semigroup Forum 44 Linear Algebra and its Applications 43 Annali di Matematica Pura ed Applicata. Serie Quarta 40 Israel Journal of Mathematics 40 Communications in Partial Differential Equations 39 Mathematical Notes 39 Ukrainian Mathematical Journal 36 Annales de l’Institut Fourier 34 Nonlinear Analysis. Theory, Methods & Applications 33 Archiv der Mathematik 33 Tohoku Mathematical Journal. Second Series 32 Journal of Mathematical Physics 31 Publications of the Research Institute for Mathematical Sciences, Kyoto University 29 Computers & Mathematics with Applications 28 Functional Analysis and its Applications 27 Journal d’Analyse Mathématique 27 Rendiconti del Seminario Matematico della Università di Padova 26 Journal of Mathematical Sciences (New York) 26 Proceedings of the Japan Academy 24 Inventiones Mathematicae 24 Journal of Approximation Theory 24 Bulletin of the American Mathematical Society. New Series 22 Acta Mathematica 22 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 20 Journal of Computational and Applied Mathematics 19 Journal of Soviet Mathematics 19 Results in Mathematics 19 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 19 Geometric and Functional Analysis. GAFA 18 Combinatorica 18 Complex Analysis and Operator Theory 17 Applied Mathematics and Computation 17 Applied Mathematics and Optimization 17 Journal of Combinatorial Theory. Series B 17 Systems & Control Letters 16 Journal of Number Theory 15 Mathematical Methods in the Applied Sciences 15 Annales de l’Institut Henri Poincaré. Physique Théorique 14 Discrete Mathematics 14 Rocky Mountain Journal of Mathematics 14 Czechoslovak Mathematical Journal 14 Mathematische Nachrichten 14 Theoretical Computer Science 14 Indagationes Mathematicae. New Series 14 Annali della Scuola Normale Superiore di Pisa. Scienze Fisiche e Matematiche. III. Ser 13 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 13 Journal of Multivariate Analysis 13 Monatshefte für Mathematik 13 European Journal of Combinatorics 13 Acta Applicandae Mathematicae 13 Stochastic Processes and their Applications 13 Abstract and Applied Analysis 12 Proceedings of the Japan Academy. Series A 12 Journal of Evolution Equations 11 Bulletin of the Australian Mathematical Society 11 Communications on Pure and Applied Mathematics 11 International Journal of Theoretical Physics 11 Journal of Statistical Physics 11 Mathematical Proceedings of the Cambridge Philosophical Society 11 Mathematics of Computation 11 Automatica 11 Compositio Mathematica 11 Manuscripta Mathematica 11 Numerische Mathematik 11 Probability Theory and Related Fields 11 Journal de Mathématiques Pures et Appliquées. Neuvième Série 11 Potential Analysis 10 Reports on Mathematical Physics 10 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 10 Mathematical Systems Theory 10 Journal of the American Mathematical Society 10 The Journal of Geometric Analysis 10 Russian Mathematics 9 Applicable Analysis 9 Journal of Geometry and Physics 9 Aequationes Mathematicae 9 SIAM Journal on Mathematical Analysis 9 Combinatorics, Probability and Computing 9 Differential Equations 9 Journal of Hyperbolic Differential Equations 9 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 8 Discrete Applied Mathematics 8 Letters in Mathematical Physics 8 Theoretical and Mathematical Physics 8 Chaos, Solitons and Fractals 8 The Annals of Probability ...and 392 more Serials all top 5 Cited in 61 Fields 1,233 Operator theory (47-XX) 1,000 Partial differential equations (35-XX) 568 Functional analysis (46-XX) 357 Global analysis, analysis on manifolds (58-XX) 350 Ordinary differential equations (34-XX) 300 Probability theory and stochastic processes (60-XX) 264 Number theory (11-XX) 252 Combinatorics (05-XX) 211 Quantum theory (81-XX) 151 Differential geometry (53-XX) 144 Functions of a complex variable (30-XX) 141 Measure and integration (28-XX) 141 Systems theory; control (93-XX) 134 Numerical analysis (65-XX) 129 Dynamical systems and ergodic theory (37-XX) 120 Fluid mechanics (76-XX) 115 Topological groups, Lie groups (22-XX) 106 Integral equations (45-XX) 98 Computer science (68-XX) 97 Abstract harmonic analysis (43-XX) 96 Approximations and expansions (41-XX) 87 Real functions (26-XX) 83 Statistical mechanics, structure of matter (82-XX) 71 Group theory and generalizations (20-XX) 69 Harmonic analysis on Euclidean spaces (42-XX) 66 Several complex variables and analytic spaces (32-XX) 62 Linear and multilinear algebra; matrix theory (15-XX) 60 Mechanics of deformable solids (74-XX) 54 Special functions (33-XX) 51 Optics, electromagnetic theory (78-XX) 50 Calculus of variations and optimal control; optimization (49-XX) 46 Difference and functional equations (39-XX) 42 Information and communication theory, circuits (94-XX) 38 Biology and other natural sciences (92-XX) 36 General topology (54-XX) 35 Integral transforms, operational calculus (44-XX) 35 Relativity and gravitational theory (83-XX) 32 Manifolds and cell complexes (57-XX) 31 Operations research, mathematical programming (90-XX) 28 Algebraic geometry (14-XX) 28 Convex and discrete geometry (52-XX) 28 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 27 Potential theory (31-XX) 20 Mathematical logic and foundations (03-XX) 20 Statistics (62-XX) 14 Mechanics of particles and systems (70-XX) 12 Sequences, series, summability (40-XX) 12 Geometry (51-XX) 11 Order, lattices, ordered algebraic structures (06-XX) 11 Algebraic topology (55-XX) 9 History and biography (01-XX) 8 Associative rings and algebras (16-XX) 7 Nonassociative rings and algebras (17-XX) 6 Geophysics (86-XX) 5 General and overarching topics; collections (00-XX) 5 Category theory; homological algebra (18-XX) 5 Astronomy and astrophysics (85-XX) 4 Field theory and polynomials (12-XX) 4 \(K\)-theory (19-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.