## Melrose, Richard Burt

Compute Distance To:
 Author ID: melrose.richard-b Published as: Melrose, Richard B.; Melrose, Richard; Melrose, R. B.; Melrose, R. more...less External Links: MGP · Wikidata · GND · IdRef
 Documents Indexed: 110 Publications since 1975, including 4 Books 3 Contributions as Editor · 2 Further Contributions Co-Authors: 36 Co-Authors with 74 Joint Publications 927 Co-Co-Authors
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### Co-Authors

 41 single-authored 7 Vasy, András 6 Mazzeo, Rafe R. 6 Sá Barreto, Antônio 5 Hassell, Andrew 5 Rochon, Frédéric 4 Albin, Pierre 4 Kottke, Chris 4 Mathai, Varghese 4 Wunsch, Jared 4 Zworski, Maciej 3 Guillemin, Victor W. 3 Piazza, Paolo 3 Singer, Isadore Manuel 3 Sjöstrand, Johannes 3 Uhlmann, Gunther Alberto 2 Andersson, Karl Gustav 2 Burghelea, Dan 2 Epstein, Charles Lawrence 2 Lee, John M. 2 Marvizi, Shahla 2 Mendoza, Gerardo A. 2 Mishchenko, Aleksandr Sergeevich 2 Nistor, Victor 2 Ritter, Niles 2 Taylor, Michael Eugene 2 Troitskiĭ, Evgeniĭ Vadimovich 2 Zhu, Xuwen 1 Beals, Michael 1 Bojarski, Bogdan 1 Dai, Xianzhe 1 Dimakis, Panagiotis 1 Freed, Daniel Stuart 1 Friedlander, Frederick Gerard 1 Pemberton, Malcolm 1 Rauch, Jeffrey B. 1 Weber, Andrzej
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### Serials

 7 Duke Mathematical Journal 6 Journal of Differential Geometry 6 Communications in Partial Differential Equations 5 Advances in Mathematics 5 Inventiones Mathematicae 4 Communications on Pure and Applied Mathematics 3 Acta Mathematica 3 Journal of Functional Analysis 3 IMRN. International Mathematics Research Notices 3 Séminaire Équations aux Dérivées Partielles 3 Mathematical Research Letters 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Geometric and Functional Analysis. GAFA 2 Astérisque 2 Trends in Mathematics 1 Communications in Mathematical Physics 1 Journal d’Analyse Mathématique 1 Arkiv för Matematik 1 Annales de l’Institut Fourier 1 Hokkaido Mathematical Journal 1 Journal für die Reine und Angewandte Mathematik 1 Mathematische Annalen 1 Topology 1 Transactions of the American Mathematical Society 1 $$K$$-Theory 1 Proceedings of the National Academy of Sciences of the United States of America 1 Communications in Analysis and Geometry 1 Journées Équations aux Dérivées Partielles (Saint-Jean-de-Monts) 1 Serdica Mathematical Journal 1 The Asian Journal of Mathematics 1 Geometry & Topology 1 Annals of Mathematics. Second Series 1 Algebraic & Geometric Topology 1 Bulletin of the American Mathematical Society 1 The IMA Volumes in Mathematics and its Applications 1 Research Notes in Mathematics 1 Analysis & PDE 1 Journal of Topology and Analysis
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### Fields

 69 Partial differential equations (35-XX) 69 Global analysis, analysis on manifolds (58-XX) 14 Operator theory (47-XX) 12 Differential geometry (53-XX) 8 $$K$$-theory (19-XX) 6 Several complex variables and analytic spaces (32-XX) 6 Manifolds and cell complexes (57-XX) 5 Quantum theory (81-XX) 4 Functional analysis (46-XX) 4 Algebraic topology (55-XX) 4 Optics, electromagnetic theory (78-XX) 3 General and overarching topics; collections (00-XX) 3 Algebraic geometry (14-XX) 3 Dynamical systems and ergodic theory (37-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 1 Category theory; homological algebra (18-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Ordinary differential equations (34-XX) 1 Numerical analysis (65-XX) 1 Relativity and gravitational theory (83-XX)

### Citations contained in zbMATH Open

101 Publications have been cited 2,757 times in 1,546 Documents Cited by Year
The Atiyah-Patodi-Singer index theorem. Zbl 0796.58050
Melrose, Richard B.
1993
Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature. Zbl 0636.58034
Mazzeo, Rafe R.; Melrose, Richard B.
1987
Geometric scattering theory. Zbl 0849.58071
Melrose, Richard B.
1995
Spectral and scattering theory for the Laplacian on asymptotically Euclidean spaces. Zbl 0837.35107
Melrose, Richard B.
1994
Singularities of boundary value problems. I. Zbl 0368.35020
Melrose, R. B.; Sjöstrand, J.
1978
Calculus of conormal distributions on manifolds with corners. Zbl 0754.58035
Melrose, Richard B.
1992
Transformation of boundary problems. Zbl 0492.58023
Melrose, Richard B.
1981
Singularities of boundary value problems. II. Zbl 0546.35083
Melrose, R. B.; Sjöstrand, J.
1982
Lagrangian intersection and the Cauchy problem. Zbl 0396.58006
Melrose, R. B.; Uhlmann, G. A.
1979
Near peak scattering and the corrected Kirchhoff approximation for a convex obstacle. Zbl 0591.58034
Melrose, Richard B.; Taylor, Michael E.
1985
Pseudodifferential operators on manifolds with fibred boundaries. Zbl 1125.58304
Mazzeo, Rafe; Melrose, Richard B.
1998
Singularities and energy decay in acoustical scattering. Zbl 0415.35050
Melrose, R. B.
1979
Resolvent of the Laplacian on strictly pseudoconvex domains. Zbl 0758.32010
Epstein, C. L.; Melrose, R. B.; Mendoza, G. A.
1991
Boundary behaviour of the complex Monge-Ampère equation. Zbl 0496.35042
Lee, John; Melrose, Richard
1982
Equivalence of glancing hyper-surfaces. Zbl 0354.53033
Melrose, R. B.
1976
Interaction of nonlinear progressing waves for semilinear wave equations. Zbl 0575.35063
Melrose, Richard; Ritter, Niles
1985
The propagation of singularities along gliding rays. Zbl 0373.35053
Andersson, K. G.; Melrose, R. B.
1977
Microlocal parametrices for diffractive boundary value problems. Zbl 0368.35055
Melrose, Richard B.
1975
Scattering metrics and geodesic flow at infinity. Zbl 0855.58058
Melrose, Richard; Zworski, Maciej
1996
The Poisson summation formula for manifolds with boundary. Zbl 0421.35082
Guillemin, Victor; Melrose, Richard
1979
Families of Dirac operators, boundaries and the $$B$$-calculus. Zbl 0955.58020
Melrose, Richard B.; Piazza, Paolo
1997
Polynomial bound on the number of scattering poles. Zbl 0535.35067
Melrose, Richard
1983
Analytic $$K$$-theory on manifolds with corners. Zbl 0761.55002
Melrose, Richard B.; Piazza, Paolo
1992
The adiabatic limit, Hodge cohomology and Leray’s spectral sequence for a fibration. Zbl 0702.58007
Mazzeo, Rafe R.; Melrose, Richard B.
1990
$$K$$-theory of $$C^*$$-algebras of b-pseudodifferential operators. Zbl 0898.46060
Melrose, R.; Nistor, V.
1998
Weyl asymptotics for the phase in obstacle scattering. Zbl 0686.35089
Melrose, Richard B.
1988
Spectral invariants of convex planar regions. Zbl 0492.53033
Marvizi, Shahla; Melrose, Richard
1982
Pseudodifferential operators, corners and singular limits. Zbl 0743.58033
Melrose, Richard B.
1991
Analytic surgery and the accumulation of eigenvalues. Zbl 0854.58039
Hassell, Andrew; Mazzeo, Rafe; Melrose, Richard B.
1995
Asymptotics of solutions of the wave equation on de Sitter-Schwarzschild space. Zbl 1286.35145
Melrose, Richard; Barreto, Antônio Sá; Vasy, András
2014
The eta invariant and families of pseudodifferential operators. Zbl 0934.58025
Melrose, Richard B.
1995
Propagation of singularities for the wave equation on conic manifolds. Zbl 1088.58011
Melrose, Richard; Wunsch, Jared
2004
Microlocal structure of involutive conical refraction. Zbl 0422.58026
Melrose, R. B.; Uhlmann, G. A.
1979
Scattering theory and the trace of the wave group. Zbl 0525.47007
Melrose, Richard
1982
An index theorem for families of Dirac operators on odd-dimensional manifolds with boundary. Zbl 0920.58053
Melrose, Richard B.; Piazza, Paolo
1997
Weyl’s conjecture for manifolds with concave boundary. Zbl 0436.58024
Melrose, R. B.
1980
Index in $$K$$-theory for families of fibred cusp operators. Zbl 1126.58010
Melrose, Richard; Rochon, Frédéric
2006
Spectral and scattering theory for symbolic potentials of order zero. Zbl 1038.35085
Hassell, Andrew; Melrose, Richard; Vasy, András
2004
Analytic surgery and the eta invariant. Zbl 0838.57022
Mazzeo, R. R.; Melrose, R. B.
1995
The index of projective families of elliptic operators. Zbl 1083.58021
Mathai, Varghese; Melrose, Richard B.; Singer, Isadore M.
2005
Interaction of progressing waves for semilinear wave equations. II. Zbl 0653.35058
Melrose, Richard B.; Ritter, Niles
1987
The Cauchy problem for effectively hyperbolic operators. Zbl 0544.35094
Melrose, Richard
1983
Propagation of singularities for the wave equation on edge manifolds. Zbl 1147.58029
Melrose, Richard; Vasy, András; Wunsch, Jared
2008
A mod $$k$$ index theorem. Zbl 0760.58039
Freed, Daniel S.; Melrose, Richard B.
1992
Contact degree and the index of Fourier integral operators. Zbl 0929.58012
Epstein, Charles; Melrose, Richard
1998
Forward scattering by a convex obstacle. Zbl 0435.35066
Melrose, R. B.
1980
Equivalence of glancing hypersurfaces. II. Zbl 0472.53045
Melrose, R. B.
1981
Local Fourier-Airy integral operators. Zbl 0368.35054
Melrose, Richard B.
1975
Polynomial bound on the distribution of poles in scattering by an obstacle. Zbl 0621.35073
Melrose, Richard
1984
Analytic continuation and semiclassical resolvent estimates on asymptotically hyperbolic spaces. Zbl 1323.58020
Melrose, Richard; Barreto, Antônio Sá; Vasy, András
2014
Microlocal propagation near radial points and scattering for symbolic potentials of order zero. Zbl 1152.35454
Hassell, Andrew; Melrose, Richard; Vasy, András
2008
The radiation pattern of a diffracted wave near the shadow boundary. Zbl 0632.35056
Melrose, Richard B.; Taylor, Michael E.
1986
The wave equation for a hypoelliptic operator with symplectic characteristics of codimension two. Zbl 0599.35139
Melrose, Richard B.
1985
Fractional analytic index. Zbl 1115.58021
Mathai, V.; Melrose, R. B.; Singer, I. M.
2006
The wave front set of the solution of a simple initial-boundary value problem with glancing rays. II. Zbl 0356.35056
Friedlander, F. G.; Melrose, R. B.
1977
A cohomological invariant of discrete dynamical systems. Zbl 0482.58032
Guillemin, Victor; Melrose, Richard
1981
A signature formula for manifolds with corners of codimension two. Zbl 0883.58038
Hassell, Andrew; Mazzeo, Rafe; Melrose, Richard B.
1997
Airy operators. Zbl 0384.35052
Melrose, R. B.
1978
Adiabatic limit, heat kernel and analytic torsion. Zbl 1318.58019
Dai, Xianzhe; Melrose, Richard B.
2012
Generalized blow-up of corners and fiber products. Zbl 1372.57042
Kottke, Chris; Melrose, Richard B.
2015
The trace of the wave group. Zbl 0547.35095
Melrose, Richard
1984
Semi-linear diffraction of conormal waves. Zbl 0902.35004
Melrose, Richard B.; Sá Barreto, Antônio; Zworski, Maciej
1996
An inverse spectral result for elliptical regions of $$\mathbb{R}^2$$. Zbl 0415.35062
Guillemin, Victor; Melrose, Richard
1979
Families index for pseudodifferential operators on manifolds with boundary. Zbl 1086.58011
Melrose, Richard; Rochon, Frédéric
2004
The index of projective families of elliptic operators: the decomposable case. Zbl 1207.19006
Mathai, Varghese; Melrose, Richard B.; Singer, Isadore M.
2009
Fredholm realizations of elliptic symbols on manifolds with boundary. Zbl 1161.58011
Albin, Pierre; Melrose, Richard
2009
Normal self-intersections of the characteristic variety. Zbl 0336.35017
Melrose, Richard B.
1975
Generalized backscattering and the Lax-Phillips transform. Zbl 1199.35270
Melrose, R.; Uhlmann, G.
2008
Propagation for the wave group of a positive subelliptic second-order differential operator. Zbl 0696.35064
Melrose, Richard
1986
Resolution of smooth group actions. Zbl 1218.58009
Albin, Pierre; Melrose, Richard
2011
Fibrations, compactifications and algebras of pseudodifferential operators. Zbl 0853.35142
Melrose, Richard B.
1996
Diffraction of singularities for the wave equation on manifolds with corners. Zbl 1277.35004
Melrose, Richard; Vasy, András; Wunsch, Jared
2013
Differential boundary value problems of principal type. Zbl 0447.35053
Melrose, R. B.
1979
Interaction of progressing waves through a nonlinear potential. Zbl 0554.35085
Melrose, R. B.
1984
The Cauchy problem with polynomial growth conditions for partial differential operators with constant coefficients. Zbl 0337.35012
Melrose, R. B.
1975
Loop-fusion cohomology and transgression. Zbl 1331.55002
Kottke, Chris; Melrose, Richard B.
2015
Nonlinear interaction of a cusp and a plane. Zbl 0847.35086
Melrose, Richard B.; Sá Barreto, Antônio
1995
Star products and local line bundles. Zbl 1061.47064
Melrose, Richard
2004
Geometric optics and the bottom of the spectrum. Zbl 0889.35129
Melrose, Richard B.
1997
Singularities of solutions to boundary value problems. Zbl 0452.35120
Melrose, Richard B.
1980
Hypoelliptic operators with characteristic variety of codimension two and the wave equation. Zbl 0468.35032
Melrose, R. B.
1980
Semilinear waves with cusp singularities. Zbl 0656.35098
Melrose, Richard B.
1987
Propagation of singularities along gliding rays. Zbl 0358.35048
1977
Singularities and the wave equation on conic spaces. Zbl 1122.58302
Melrose, Richard B.; Wunsch, Jared
2001
Periodicity and the determinant bundle. Zbl 1130.58013
Melrose, Richard; Rochon, Frédéric
2007
Resolution of the canonical fiber metrics for a Lefschetz fibration. Zbl 1404.30047
Melrose, Richard; Zhu, Xuwen
2018
Geometry of pseudodifferential algebra bundles and Fourier integral operators. Zbl 1397.58015
Mathai, Varghese; Melrose, Richard B.
2017
Relative Chern character, boundaries and index formulas. Zbl 1207.58020
Albin, Pierre; Melrose, Richard
2009
The Cauchy problem and propagation of singularities. Zbl 0599.35095
Melrose, Richard
1984
Periodic solutions of certain nonlinear autonomous wave equations. Zbl 0315.35007
Melrose, Richard B.; Pemberton, Malcolm
1975
Conormality, cusps and nonlinear interaction. Zbl 0794.35005
Melrose, Richard B.
1991
Scattering theory for strictly pseudoconvex domains. Zbl 0927.37034
Melrose, Richard
1999
Eta forms and the odd pseudodifferential families index. Zbl 1239.58019
Melrose, Richard; Rochon, Frédéric
2011
Transformation methods for boundary value problems. Zbl 0477.35087
Melrose, Richard B.
1981
Elliptic boundary problems on spaces with conic points. Zbl 0481.35004
Melrose, Richard B.; Mendoza, Gerardo A.
1981
Some spectrally isolated convex planar regions. Zbl 0504.53040
Marvizi, Shahla; Melrose, Richard B.
1982
Homology and the Heisenberg algebra. Joint work with C. Epstein and G. Mendoza. Zbl 1054.58013
Melrose, Richard
1997
Propagation de singularites pour des problèmes aux limites d’ordre 2. Zbl 0383.35043
Melrose, R. B.; Sjöstrand, J.
1978
Boundaries, eta invariant and the determinant bundle. Zbl 1196.58015
Melrose, Richard; Rochon, Frédéric
2008
Equivariant $$K$$-theory and resolution. I: Abelian actions. Zbl 07225720
Dimakis, Panagiotis; Melrose, Richard
2020
Equivariant $$K$$-theory and resolution. I: Abelian actions. Zbl 07225720
Dimakis, Panagiotis; Melrose, Richard
2020
Resolution of the canonical fiber metrics for a Lefschetz fibration. Zbl 1404.30047
Melrose, Richard; Zhu, Xuwen
2018
Geometry of pseudodifferential algebra bundles and Fourier integral operators. Zbl 1397.58015
Mathai, Varghese; Melrose, Richard B.
2017
Generalized blow-up of corners and fiber products. Zbl 1372.57042
Kottke, Chris; Melrose, Richard B.
2015
Loop-fusion cohomology and transgression. Zbl 1331.55002
Kottke, Chris; Melrose, Richard B.
2015
Asymptotics of solutions of the wave equation on de Sitter-Schwarzschild space. Zbl 1286.35145
Melrose, Richard; Barreto, Antônio Sá; Vasy, András
2014
Analytic continuation and semiclassical resolvent estimates on asymptotically hyperbolic spaces. Zbl 1323.58020
Melrose, Richard; Barreto, Antônio Sá; Vasy, András
2014
Diffraction of singularities for the wave equation on manifolds with corners. Zbl 1277.35004
Melrose, Richard; Vasy, András; Wunsch, Jared
2013
Adiabatic limit, heat kernel and analytic torsion. Zbl 1318.58019
Dai, Xianzhe; Melrose, Richard B.
2012
Resolution of smooth group actions. Zbl 1218.58009
Albin, Pierre; Melrose, Richard
2011
Eta forms and the odd pseudodifferential families index. Zbl 1239.58019
Melrose, Richard; Rochon, Frédéric
2011
Fredholm realizations of elliptic symbols on manifolds with boundary. II: Fibered boundary. Zbl 1217.58014
Albin, Pierre; Melrose, Richard
2010
The index of projective families of elliptic operators: the decomposable case. Zbl 1207.19006
Mathai, Varghese; Melrose, Richard B.; Singer, Isadore M.
2009
Fredholm realizations of elliptic symbols on manifolds with boundary. Zbl 1161.58011
Albin, Pierre; Melrose, Richard
2009
Relative Chern character, boundaries and index formulas. Zbl 1207.58020
Albin, Pierre; Melrose, Richard
2009
Propagation of singularities for the wave equation on edge manifolds. Zbl 1147.58029
Melrose, Richard; Vasy, András; Wunsch, Jared
2008
Microlocal propagation near radial points and scattering for symbolic potentials of order zero. Zbl 1152.35454
Hassell, Andrew; Melrose, Richard; Vasy, András
2008
Generalized backscattering and the Lax-Phillips transform. Zbl 1199.35270
Melrose, R.; Uhlmann, G.
2008
Boundaries, eta invariant and the determinant bundle. Zbl 1196.58015
Melrose, Richard; Rochon, Frédéric
2008
Periodicity and the determinant bundle. Zbl 1130.58013
Melrose, Richard; Rochon, Frédéric
2007
Index in $$K$$-theory for families of fibred cusp operators. Zbl 1126.58010
Melrose, Richard; Rochon, Frédéric
2006
Fractional analytic index. Zbl 1115.58021
Mathai, V.; Melrose, R. B.; Singer, I. M.
2006
The index of projective families of elliptic operators. Zbl 1083.58021
Mathai, Varghese; Melrose, Richard B.; Singer, Isadore M.
2005
Propagation of singularities for the wave equation on conic manifolds. Zbl 1088.58011
Melrose, Richard; Wunsch, Jared
2004
Spectral and scattering theory for symbolic potentials of order zero. Zbl 1038.35085
Hassell, Andrew; Melrose, Richard; Vasy, András
2004
Families index for pseudodifferential operators on manifolds with boundary. Zbl 1086.58011
Melrose, Richard; Rochon, Frédéric
2004
Star products and local line bundles. Zbl 1061.47064
Melrose, Richard
2004
Singularities and the wave equation on conic spaces. Zbl 1122.58302
Melrose, Richard B.; Wunsch, Jared
2001
Scattering theory for strictly pseudoconvex domains. Zbl 0927.37034
Melrose, Richard
1999
Pseudodifferential operators on manifolds with fibred boundaries. Zbl 1125.58304
Mazzeo, Rafe; Melrose, Richard B.
1998
$$K$$-theory of $$C^*$$-algebras of b-pseudodifferential operators. Zbl 0898.46060
Melrose, R.; Nistor, V.
1998
Contact degree and the index of Fourier integral operators. Zbl 0929.58012
Epstein, Charles; Melrose, Richard
1998
Families of Dirac operators, boundaries and the $$B$$-calculus. Zbl 0955.58020
Melrose, Richard B.; Piazza, Paolo
1997
An index theorem for families of Dirac operators on odd-dimensional manifolds with boundary. Zbl 0920.58053
Melrose, Richard B.; Piazza, Paolo
1997
A signature formula for manifolds with corners of codimension two. Zbl 0883.58038
Hassell, Andrew; Mazzeo, Rafe; Melrose, Richard B.
1997
Geometric optics and the bottom of the spectrum. Zbl 0889.35129
Melrose, Richard B.
1997
Homology and the Heisenberg algebra. Joint work with C. Epstein and G. Mendoza. Zbl 1054.58013
Melrose, Richard
1997
Scattering metrics and geodesic flow at infinity. Zbl 0855.58058
Melrose, Richard; Zworski, Maciej
1996
Semi-linear diffraction of conormal waves. Zbl 0902.35004
Melrose, Richard B.; Sá Barreto, Antônio; Zworski, Maciej
1996
Fibrations, compactifications and algebras of pseudodifferential operators. Zbl 0853.35142
Melrose, Richard B.
1996
Geometric scattering theory. Zbl 0849.58071
Melrose, Richard B.
1995
Analytic surgery and the accumulation of eigenvalues. Zbl 0854.58039
Hassell, Andrew; Mazzeo, Rafe; Melrose, Richard B.
1995
The eta invariant and families of pseudodifferential operators. Zbl 0934.58025
Melrose, Richard B.
1995
Analytic surgery and the eta invariant. Zbl 0838.57022
Mazzeo, R. R.; Melrose, R. B.
1995
Nonlinear interaction of a cusp and a plane. Zbl 0847.35086
Melrose, Richard B.; Sá Barreto, Antônio
1995
Spectral and scattering theory for the Laplacian on asymptotically Euclidean spaces. Zbl 0837.35107
Melrose, Richard B.
1994
The Atiyah-Patodi-Singer index theorem. Zbl 0796.58050
Melrose, Richard B.
1993
Calculus of conormal distributions on manifolds with corners. Zbl 0754.58035
Melrose, Richard B.
1992
Analytic $$K$$-theory on manifolds with corners. Zbl 0761.55002
Melrose, Richard B.; Piazza, Paolo
1992
A mod $$k$$ index theorem. Zbl 0760.58039
Freed, Daniel S.; Melrose, Richard B.
1992
Resolvent of the Laplacian on strictly pseudoconvex domains. Zbl 0758.32010
Epstein, C. L.; Melrose, R. B.; Mendoza, G. A.
1991
Pseudodifferential operators, corners and singular limits. Zbl 0743.58033
Melrose, Richard B.
1991
Conormality, cusps and nonlinear interaction. Zbl 0794.35005
Melrose, Richard B.
1991
The adiabatic limit, Hodge cohomology and Leray’s spectral sequence for a fibration. Zbl 0702.58007
Mazzeo, Rafe R.; Melrose, Richard B.
1990
Weyl asymptotics for the phase in obstacle scattering. Zbl 0686.35089
Melrose, Richard B.
1988
Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature. Zbl 0636.58034
Mazzeo, Rafe R.; Melrose, Richard B.
1987
Interaction of progressing waves for semilinear wave equations. II. Zbl 0653.35058
Melrose, Richard B.; Ritter, Niles
1987
Semilinear waves with cusp singularities. Zbl 0656.35098
Melrose, Richard B.
1987
The radiation pattern of a diffracted wave near the shadow boundary. Zbl 0632.35056
Melrose, Richard B.; Taylor, Michael E.
1986
Propagation for the wave group of a positive subelliptic second-order differential operator. Zbl 0696.35064
Melrose, Richard
1986
Near peak scattering and the corrected Kirchhoff approximation for a convex obstacle. Zbl 0591.58034
Melrose, Richard B.; Taylor, Michael E.
1985
Interaction of nonlinear progressing waves for semilinear wave equations. Zbl 0575.35063
Melrose, Richard; Ritter, Niles
1985
The wave equation for a hypoelliptic operator with symplectic characteristics of codimension two. Zbl 0599.35139
Melrose, Richard B.
1985
Polynomial bound on the distribution of poles in scattering by an obstacle. Zbl 0621.35073
Melrose, Richard
1984
The trace of the wave group. Zbl 0547.35095
Melrose, Richard
1984
Interaction of progressing waves through a nonlinear potential. Zbl 0554.35085
Melrose, R. B.
1984
The Cauchy problem and propagation of singularities. Zbl 0599.35095
Melrose, Richard
1984
Polynomial bound on the number of scattering poles. Zbl 0535.35067
Melrose, Richard
1983
The Cauchy problem for effectively hyperbolic operators. Zbl 0544.35094
Melrose, Richard
1983
Singularities of boundary value problems. II. Zbl 0546.35083
Melrose, R. B.; Sjöstrand, J.
1982
Boundary behaviour of the complex Monge-Ampère equation. Zbl 0496.35042
Lee, John; Melrose, Richard
1982
Spectral invariants of convex planar regions. Zbl 0492.53033
Marvizi, Shahla; Melrose, Richard
1982
Scattering theory and the trace of the wave group. Zbl 0525.47007
Melrose, Richard
1982
Some spectrally isolated convex planar regions. Zbl 0504.53040
Marvizi, Shahla; Melrose, Richard B.
1982
Transformation of boundary problems. Zbl 0492.58023
Melrose, Richard B.
1981
Equivalence of glancing hypersurfaces. II. Zbl 0472.53045
Melrose, R. B.
1981
A cohomological invariant of discrete dynamical systems. Zbl 0482.58032
Guillemin, Victor; Melrose, Richard
1981
Transformation methods for boundary value problems. Zbl 0477.35087
Melrose, Richard B.
1981
Elliptic boundary problems on spaces with conic points. Zbl 0481.35004
Melrose, Richard B.; Mendoza, Gerardo A.
1981
Weyl’s conjecture for manifolds with concave boundary. Zbl 0436.58024
Melrose, R. B.
1980
Forward scattering by a convex obstacle. Zbl 0435.35066
Melrose, R. B.
1980
Singularities of solutions to boundary value problems. Zbl 0452.35120
Melrose, Richard B.
1980
Hypoelliptic operators with characteristic variety of codimension two and the wave equation. Zbl 0468.35032
Melrose, R. B.
1980
Lagrangian intersection and the Cauchy problem. Zbl 0396.58006
Melrose, R. B.; Uhlmann, G. A.
1979
Singularities and energy decay in acoustical scattering. Zbl 0415.35050
Melrose, R. B.
1979
The Poisson summation formula for manifolds with boundary. Zbl 0421.35082
Guillemin, Victor; Melrose, Richard
1979
Microlocal structure of involutive conical refraction. Zbl 0422.58026
Melrose, R. B.; Uhlmann, G. A.
1979
An inverse spectral result for elliptical regions of $$\mathbb{R}^2$$. Zbl 0415.35062
Guillemin, Victor; Melrose, Richard
1979
Differential boundary value problems of principal type. Zbl 0447.35053
Melrose, R. B.
1979
Singularities of boundary value problems. I. Zbl 0368.35020
Melrose, R. B.; Sjöstrand, J.
1978
Airy operators. Zbl 0384.35052
Melrose, R. B.
1978
Propagation de singularites pour des problèmes aux limites d’ordre 2. Zbl 0383.35043
Melrose, R. B.; Sjöstrand, J.
1978
The propagation of singularities along gliding rays. Zbl 0373.35053
Andersson, K. G.; Melrose, R. B.
1977
The wave front set of the solution of a simple initial-boundary value problem with glancing rays. II. Zbl 0356.35056
Friedlander, F. G.; Melrose, R. B.
1977
Propagation of singularities along gliding rays. Zbl 0358.35048
1977
Equivalence of glancing hyper-surfaces. Zbl 0354.53033
Melrose, R. B.
1976
Microlocal parametrices for diffractive boundary value problems. Zbl 0368.35055
Melrose, Richard B.
1975
Local Fourier-Airy integral operators. Zbl 0368.35054
Melrose, Richard B.
1975
Normal self-intersections of the characteristic variety. Zbl 0336.35017
Melrose, Richard B.
1975
The Cauchy problem with polynomial growth conditions for partial differential operators with constant coefficients. Zbl 0337.35012
Melrose, R. B.
1975
...and 1 more Documents
all top 5

### Cited by 1,137 Authors

 44 Vasy, András 34 Melrose, Richard Burt 28 Uhlmann, Gunther Alberto 28 Zworski, Maciej 27 Guillarmou, Colin 24 Sá Barreto, Antônio 22 Hassell, Andrew 21 Nistor, Victor 21 Petkov, Vesselin M. 21 Rochon, Frédéric 18 Mazzeo, Rafe R. 17 Moroianu, Sergiu 17 Vertman, Boris 16 Stoyanov, Luchezar N. 15 Loya, Paul A. 15 Wang, Yiran 15 Wunsch, Jared 14 Albin, Pierre 14 Burq, Nicolas 14 Coriasco, Sandro 14 Park, Jinsung 13 Lassas, Matti J. 13 Miranda, Eva 13 Schrohe, Elmar 13 Sjöstrand, Johannes 12 Greenleaf, Allan 12 Piazza, Paolo 12 Schulze, Bert-Wolfgang 12 Spence, Euan A. 11 Christiansen, Tanya J. 11 Hintz, Peter 11 Perry, Peter A. 10 Dyatlov, Semyon 10 Krainer, Thomas 10 Lauter, Robert 10 Savin, Anton Yur’evich 10 Stefanov, Plamen D. 10 Vodev, Georgi 10 Zelditch, Steve 9 Colin de Verdière, Yves 9 Kaloshin, Vadim Yu. 9 Leichtnam, Eric 9 Sogge, Christopher D. 9 Zhang, Junyong 8 Baskin, Dean 8 Borthwick, David 8 Felea, Raluca 8 Galkowski, Jeffrey 8 Lebeau, Gilles 8 Lescure, Jean-Marie 8 Mendoza, Gerardo A. 8 Naud, Frédéric 8 Ponge, Raphaël S. 8 Taylor, Michael Eugene 7 Aloui, Lassaad 7 Chen, Hua 7 Chen, Xi 7 Epstein, Charles Lawrence 7 Guillemin, Victor W. 7 Hillairet, Luc 7 Joshi, Mark S. 7 Kottke, Chris 7 Novikov, Roman G. 7 Popov, Georgi St. 7 Rowlett, Julie 7 Salo, Mikko 7 Skibsted, Erik 7 Smyshlyaev, Valery P. 7 Strohmaier, Alexander 7 Williams, Mark 6 Ascanelli, Alessia 6 Barbagallo, Annamaria 6 Carrillo-Rouse, Paulo 6 Dai, Xianzhe 6 Debord, Claire 6 Eskin, Gregory 6 Esposito, Vincenzo 6 Gannot, Oran 6 Gell-Redman, Jesse 6 González, María del Mar 6 Hislop, Peter D. 6 Kim, Seunghyeok 6 Lesch, Matthias 6 Matsumoto, Yoshihiko 6 Nishitani, Tatsuo 6 Rauch, Jeffrey B. 6 Royer, Julien 6 Sternin, Boris Yur’evich 6 Tabachnikov, Serge L. 6 Zhang, Weiping 5 Ammann, Bernd Eberhard 5 Bahuaud, Eric 5 Benameur, Moulay-Tahar 5 Biquard, Olivier 5 Bony, Jean-François 5 Bouclet, Jean-Marc 5 Bunke, Ulrich 5 Cappiello, Marco 5 Carron, Gilles 5 Campos de Carvalho, Catarina ...and 1,037 more Authors
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### Cited in 232 Serials

 119 Communications in Partial Differential Equations 102 Journal of Functional Analysis 77 Communications in Mathematical Physics 60 Duke Mathematical Journal 53 Advances in Mathematics 50 Transactions of the American Mathematical Society 49 Annales de l’Institut Fourier 44 The Journal of Geometric Analysis 29 Journal of Geometry and Physics 28 Mathematische Annalen 26 Journal of Differential Equations 24 Journal of Mathematical Analysis and Applications 24 Annales Henri Poincaré 22 Journal d’Analyse Mathématique 21 Mathematische Zeitschrift 19 Inventiones Mathematicae 18 Journal of Mathematical Physics 16 Annals of Global Analysis and Geometry 16 Geometric and Functional Analysis. GAFA 15 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 15 Mathematische Nachrichten 15 Proceedings of the American Mathematical Society 14 Journal de Mathématiques Pures et Appliquées. Neuvième Série 14 Annals of Mathematics. Second Series 13 Annales de l’Institut Henri Poincaré. Physique Théorique 13 Geometry & Topology 13 Comptes Rendus. Mathématique. Académie des Sciences, Paris 12 Journal für die Reine und Angewandte Mathematik 12 Journal of the American Mathematical Society 12 Journal of Spectral Theory 11 SIAM Journal on Mathematical Analysis 11 Calculus of Variations and Partial Differential Equations 11 Journal of Pseudo-Differential Operators and Applications 10 Acta Mathematica 10 Analysis & PDE 9 Numerische Mathematik 9 Bulletin of the American Mathematical Society. New Series 9 Journal of the European Mathematical Society (JEMS) 8 Communications on Pure and Applied Mathematics 8 Integral Equations and Operator Theory 8 Proceedings of the Japan Academy. Series A 8 The Journal of Fourier Analysis and Applications 8 Journal of Noncommutative Geometry 8 Journal of $$K$$-Theory 7 Letters in Mathematical Physics 7 Mathematical Proceedings of the Cambridge Philosophical Society 7 Arkiv för Matematik 7 Annali di Matematica Pura ed Applicata. Serie Quarta 7 Bulletin de la Société Mathématique de France 7 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 7 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 7 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 7 Journal of the Institute of Mathematics of Jussieu 6 Inverse Problems 6 Israel Journal of Mathematics 6 Journal of the Mathematical Society of Japan 6 Memoirs of the American Mathematical Society 6 Monatshefte für Mathematik 6 Differential Geometry and its Applications 6 Inverse Problems and Imaging 6 Pure and Applied Analysis 5 Journal of Computational Physics 5 Compositio Mathematica 5 Functional Analysis and its Applications 5 Pacific Journal of Mathematics 5 $$K$$-Theory 5 Journal of Mathematical Sciences (New York) 5 Discrete and Continuous Dynamical Systems 5 Regular and Chaotic Dynamics 5 Communications in Contemporary Mathematics 5 Science China. Mathematics 5 Séminaire Laurent Schwartz. EDP et Applications 4 Applicable Analysis 4 Nonlinearity 4 Reviews in Mathematical Physics 4 Journal of Soviet Mathematics 4 Publications of the Research Institute for Mathematical Sciences, Kyoto University 4 Siberian Mathematical Journal 4 Ergodic Theory and Dynamical Systems 4 Acta Applicandae Mathematicae 4 Mémoires de la Société Mathématique de France. Nouvelle Série 4 Acta Mathematica Sinica. New Series 4 Russian Journal of Mathematical Physics 4 Journal of Hyperbolic Differential Equations 4 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 4 Bulletin of Mathematical Sciences 4 Nonlinear Analysis. Theory, Methods & Applications 3 Archive for Rational Mechanics and Analysis 3 Classical and Quantum Gravity 3 Mathematical Methods in the Applied Sciences 3 Rocky Mountain Journal of Mathematics 3 Wave Motion 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 3 Journal of Computational and Applied Mathematics 3 Manuscripta Mathematica 3 Revista Matemática Iberoamericana 3 International Journal of Mathematics 3 SIAM Journal on Applied Mathematics 3 Indagationes Mathematicae. New Series 3 Bulletin des Sciences Mathématiques ...and 132 more Serials
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### Cited in 54 Fields

 890 Partial differential equations (35-XX) 708 Global analysis, analysis on manifolds (58-XX) 308 Differential geometry (53-XX) 208 Operator theory (47-XX) 164 Quantum theory (81-XX) 94 Several complex variables and analytic spaces (32-XX) 92 Dynamical systems and ergodic theory (37-XX) 74 Functional analysis (46-XX) 71 $$K$$-theory (19-XX) 61 Relativity and gravitational theory (83-XX) 48 Optics, electromagnetic theory (78-XX) 46 Manifolds and cell complexes (57-XX) 43 Numerical analysis (65-XX) 36 Topological groups, Lie groups (22-XX) 35 Harmonic analysis on Euclidean spaces (42-XX) 34 Number theory (11-XX) 32 Algebraic topology (55-XX) 28 Mechanics of deformable solids (74-XX) 25 Algebraic geometry (14-XX) 25 Ordinary differential equations (34-XX) 25 Systems theory; control (93-XX) 22 Functions of a complex variable (30-XX) 22 Integral transforms, operational calculus (44-XX) 18 Mechanics of particles and systems (70-XX) 17 Fluid mechanics (76-XX) 14 Potential theory (31-XX) 14 Abstract harmonic analysis (43-XX) 13 Probability theory and stochastic processes (60-XX) 7 Biology and other natural sciences (92-XX) 6 Group theory and generalizations (20-XX) 6 Integral equations (45-XX) 6 Geophysics (86-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Nonassociative rings and algebras (17-XX) 4 Category theory; homological algebra (18-XX) 4 Measure and integration (28-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 Geometry (51-XX) 3 Combinatorics (05-XX) 3 General topology (54-XX) 3 Statistical mechanics, structure of matter (82-XX) 3 Astronomy and astrophysics (85-XX) 2 Real functions (26-XX) 2 Special functions (33-XX) 2 Approximations and expansions (41-XX) 2 Convex and discrete geometry (52-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Commutative algebra (13-XX) 1 Associative rings and algebras (16-XX) 1 Difference and functional equations (39-XX) 1 Computer science (68-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Information and communication theory, circuits (94-XX)

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