Ralph S. Phillips

Ralph S. Phillips's AcademicInfluence.com Rankings

Ralph S. Phillips

Mathematics

#789

World Rank

#1421

Historical Rank

#344

USA Rank

Measure Theory

#1074

World Rank

#1380

Historical Rank

#392

USA Rank

mathematics Degrees

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Mathematics

Why Is Ralph S. Phillips Influential?

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According to Wikipedia, Ralph Saul Phillips was an American mathematician and academic known for his contributions to functional analysis, scattering theory, and servomechanisms. He served as a Professor of mathematics at Stanford University. He made major contributions to acoustical scattering theory in collaboration with Peter Lax, proving remarkable results on local energy decay and the connections between poles of the scattering matrix and the analytic properties of the resolvent. With Lax, he coauthored the widely referred book on scattering theory titled Scattering Theory for Automorphic Functions. Phillips received the 1997 Leroy P. Steele Prize for Lifetime Achievement.

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Ralph S. Phillips's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Extremals of determinants of Laplacians (1988) (454)
Local boundary conditions for dissipative symmetric linear differential operators (1960) (380)
Scattering Theory for Automorphic Functions. (1967) (341)
Dissipative operators in a Banach space (1961) (338)
The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces (1982) (301)
DISSIPATIVE OPERATORS AND HYPERBOLIC SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS (1959) (250)
Exponential decay of solutions of the wave equation in the exterior of a star-shaped obstacle (1962) (207)
Hecke operators and distributing points on the sphere I (1986) (197)
Explicit expanders and the Ramanujan conjectures (1986) (175)
Compact isospectral sets of surfaces (1988) (169)
Perturbation theory for semi-groups of linear operators (1953) (168)
On cusp forms for co-finite subgroups ofPSL(2,ℝ) (1985) (138)
On the generation of semigroups of linear operators. (1952) (130)
AN INVERSION FORMULA FOR LAPLACE TRANSFORMS AND SEMI- GROUPS OF LINEAR OPERATORS' (1954) (125)
Hecke operators and distributing points on S2. II (1987) (112)
On matrices whose real linear combinations are non-singular (1965) (111)
Absolutely Convergent Fourier Expansions for Non-Commutative Normed Rings (1942) (109)
Geodesics in homology classes (1987) (107)
On Weakly Compact Subsets of a Banach Space (1943) (97)
Scattering Theory for Dissipative Hyperbolic Systems (1973) (89)
Linear Transformations (1940) (86)
Hodge theory on hyperbolic manifolds (1990) (84)
Decaying modes for the wave equation in the exterior of an obstacle (1969) (82)
Integration in a convex linear topological space (1940) (78)
The adjoint semi-group (1955) (77)
Scattering Theory for the Acoustic Equation in an Even Number of Space Dimensions (1972) (71)
Translation representations for automorphic solutions of the wave equation in non‐euclidean spaces. I (1984) (67)
Moduli space, heights and isospectral sets of plane domains* (1989) (64)
The Circle Problem in the Hyperbolic Plane (1994) (59)
Additive Set Functions and Vector Lattices (1941) (50)
Perturbation theory for the Laplacian on automorphic functions (1992) (50)
The weyl theorem and the deformation of discrete groups (1985) (50)
The laplacian for domains in hyperbolic space and limit sets of Kleinian groups (1985) (49)
The scattering of sound waves by an obstacle (1977) (48)
Dissipative hyperbolic systems (1957) (47)
PROJECTION OF THE SPACE (m) ON ITS SUBSPACE (co) (2007) (46)
A logrithmic bound on the location of the poles of the scattering matrix (1972) (46)
Semi-groups of positive contraction operators (1962) (44)
Scattering Theory for Automorphic Functions. (AM-87) (1977) (39)
An example of huygens' principle (1978) (37)
The paley-wiener theorem for the radon transform (1970) (36)
The spectrum of fermat curves (1991) (35)
Translation representations for the solution of the non‐euclidean wave equation (1979) (32)
Spectral theory for semi-groups of linear operators (1951) (31)
On symplectic mappings of contraction operators (1968) (30)
A NOTE ON THE ABSTRACT CAUCHY PROBLEM. (1954) (28)
Correction to “On matrices whose real linear combinations are nonsingular” (1966) (27)
Cusp forms for character varieties (1994) (26)
Maass cusp forms. (1985) (26)
Dissipative operators and parabolic partial differential equations (1959) (26)
On the extension problem for dissipative operators (1968) (25)
Intertwining Operators and Residues (1989) (25)
The acoustic equation with an indefinite energy form and the Schrödinger equation (1967) (24)
On the scattering frequencies of the laplace operator for exterior domains (1972) (22)
The wave equation in exterior domains (1962) (22)
Bessel Function Approximations (1950) (22)
On one-parameter semi-groups of linear transformations (1951) (21)
A characterization of euclidean spaces (1940) (19)
Compact isospectral sets of plane domains. (1988) (18)
Scattering theory for the wave equation with a short range perturbation. II (1984) (18)
Automorphic spectrum and Fermi’s Golden Rule (1992) (18)
On the spectrum of the Hecke groups (1985) (13)
Corrigendum on 'Elliptic-Parabolic Equations of the Second Order' (1968) (13)
THE ASYMPTOTIC DISTRIBUTION OF LATTICE POINTS (1981) (12)
A remark on the preceding paper of C. S. morawetz and D. ludwig (1969) (10)
Semi-groups of operators (1955) (10)
A local paley‐wiener theorem for the radon transform of L2 functions in a non‐euclidean setting (1982) (10)
ON THE INTEGRATION OF THE DIFFUSION EQUATION WITH BOUNDARY CONDITIONS( (1961) (9)
On Fourier-Stieltjes integrals (1950) (9)
Translation representations for automorphic solutions of the wave equation in non-Euclidean spaces; the case of finite volume (1985) (9)
Scattering theory for symmetric spaces of noncompact type (1993) (8)
Energy decay for the neutrino equation in the exterior of a torus (1971) (5)
Groups Of Positive Operators (1956) (5)
Scattering Theory for the Wave Equation on a Hyperbolic Manifold (1987) (5)
A note on ergodic theory (1951) (4)
Dissolving a cusp form in the presence of multiplicities (1997) (4)
Reminiscences about the 1930s (1994) (4)
The translation representation theorem (1981) (3)
Scattering theory for domains with non-smooth boundaries (1978) (3)
Perturbation theory for twisted automorphic functions (1997) (2)
A decomposition of additive set functions (1940) (2)
The Spectrum of the Laplacian for Domains in Hyperbolic Space and Limit Sets of Kleinian Groups (1984) (2)
Scattering theory for twisted automorphic functions (1998) (2)
A WEAKLY POLYHOMOGENEOUS CALCULUS FOR PSEUDODIFFERENTIAL BOUNDARY PROBLEMS (2007) (1)
7. THE SCATTERING MATRIX FOR THE AUTOMORPHIC WAVE EQUATION (1977) (1)
On a theorem due to Sz.-Nagy (1959) (1)
THE WIENER INTEGRAL AND PERTURBATION THEORY OF THE SCHRÖDINGER OPERATOR (2007) (1)
§4. THE LAPLACE-BELTRAMI OPERATOR FOR THE MODULAR GROUP (1977) (0)
3. A MODIFIED THEORY FOR SECOND ORDER EQUATIONS WITH AN INDEFINITE ENERGY FORM (1977) (0)
Scattering theory for the Hilbert modular group (1996) (0)
Lecture Series in Differential Equations, Session VI. Differential Equations in a Banach Space, (1966) (0)
ISOSPECTRAL MANIFOLDS WITH DIFFERENT LOCAL GEOMETRIES 3 (2001) (0)
LIST OF SYMBOLS (1977) (0)
9. THE SELBERG TRACE FORMULA (1977) (0)
Conjugacy classes of G(2) and spectral rigidity (1995) (0)
8. THE GENERAL CASE (1977) (0)
2. AN ABSTRACT SCATTERING THEORY (1977) (0)
5. THE AUTOMORPHIC WAVE EQUATIONS (1977) (0)
6. INCOMING AND OUTGOING SUBSPACES FOR THE AUTOMORPHIC WAVE EQUATION (1977) (0)
SCATTERING THEORY FOR HYPERBOLIC SYSTEMS (1970) (0)
Supplement to Conjugacy Classes of Γ(2) and Spectral Rigidity (1995) (0)
Correction to: Translation representation for the solution of the non-euclidean wave equation (1980) (0)
Scattering Theory for Hyperbolic Equations (1969) (0)

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