Edit Profile (opens in new tab) Melrose, Richard Burt Compute Distance To: Compute 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 all top 5 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 all top 5 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 all top 5 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) Publications by Year all cited Publications top 5 cited Publications 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 0796.58050Melrose, Richard B. 319 1993 Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature. Zbl 0636.58034Mazzeo, Rafe R.; Melrose, Richard B. 180 1987 Geometric scattering theory. Zbl 0849.58071Melrose, Richard B. 164 1995 Spectral and scattering theory for the Laplacian on asymptotically Euclidean spaces. Zbl 0837.35107Melrose, Richard B. 116 1994 Singularities of boundary value problems. I. Zbl 0368.35020Melrose, R. B.; Sjöstrand, J. 112 1978 Calculus of conormal distributions on manifolds with corners. Zbl 0754.58035Melrose, Richard B. 84 1992 Transformation of boundary problems. Zbl 0492.58023Melrose, Richard B. 74 1981 Singularities of boundary value problems. II. Zbl 0546.35083Melrose, R. B.; Sjöstrand, J. 72 1982 Lagrangian intersection and the Cauchy problem. Zbl 0396.58006Melrose, R. B.; Uhlmann, G. A. 72 1979 Near peak scattering and the corrected Kirchhoff approximation for a convex obstacle. Zbl 0591.58034Melrose, Richard B.; Taylor, Michael E. 71 1985 Pseudodifferential operators on manifolds with fibred boundaries. Zbl 1125.58304Mazzeo, Rafe; Melrose, Richard B. 68 1998 Singularities and energy decay in acoustical scattering. Zbl 0415.35050Melrose, R. B. 66 1979 Resolvent of the Laplacian on strictly pseudoconvex domains. Zbl 0758.32010Epstein, C. L.; Melrose, R. B.; Mendoza, G. A. 62 1991 Boundary behaviour of the complex Monge-Ampère equation. Zbl 0496.35042Lee, John; Melrose, Richard 60 1982 Equivalence of glancing hyper-surfaces. Zbl 0354.53033Melrose, R. B. 56 1976 Interaction of nonlinear progressing waves for semilinear wave equations. Zbl 0575.35063Melrose, Richard; Ritter, Niles 53 1985 The propagation of singularities along gliding rays. Zbl 0373.35053Andersson, K. G.; Melrose, R. B. 53 1977 Microlocal parametrices for diffractive boundary value problems. Zbl 0368.35055Melrose, Richard B. 48 1975 Scattering metrics and geodesic flow at infinity. Zbl 0855.58058Melrose, Richard; Zworski, Maciej 48 1996 The Poisson summation formula for manifolds with boundary. Zbl 0421.35082Guillemin, Victor; Melrose, Richard 40 1979 Families of Dirac operators, boundaries and the \(B\)-calculus. Zbl 0955.58020Melrose, Richard B.; Piazza, Paolo 38 1997 Polynomial bound on the number of scattering poles. Zbl 0535.35067Melrose, Richard 38 1983 Analytic \(K\)-theory on manifolds with corners. Zbl 0761.55002Melrose, Richard B.; Piazza, Paolo 37 1992 The adiabatic limit, Hodge cohomology and Leray’s spectral sequence for a fibration. Zbl 0702.58007Mazzeo, Rafe R.; Melrose, Richard B. 31 1990 \(K\)-theory of \(C^*\)-algebras of b-pseudodifferential operators. Zbl 0898.46060Melrose, R.; Nistor, V. 30 1998 Weyl asymptotics for the phase in obstacle scattering. Zbl 0686.35089Melrose, Richard B. 30 1988 Spectral invariants of convex planar regions. Zbl 0492.53033Marvizi, Shahla; Melrose, Richard 29 1982 Pseudodifferential operators, corners and singular limits. Zbl 0743.58033Melrose, Richard B. 28 1991 Analytic surgery and the accumulation of eigenvalues. Zbl 0854.58039Hassell, Andrew; Mazzeo, Rafe; Melrose, Richard B. 27 1995 Asymptotics of solutions of the wave equation on de Sitter-Schwarzschild space. Zbl 1286.35145Melrose, Richard; Barreto, Antônio Sá; Vasy, András 27 2014 The eta invariant and families of pseudodifferential operators. Zbl 0934.58025Melrose, Richard B. 26 1995 Propagation of singularities for the wave equation on conic manifolds. Zbl 1088.58011Melrose, Richard; Wunsch, Jared 25 2004 Microlocal structure of involutive conical refraction. Zbl 0422.58026Melrose, R. B.; Uhlmann, G. A. 24 1979 Scattering theory and the trace of the wave group. Zbl 0525.47007Melrose, Richard 22 1982 An index theorem for families of Dirac operators on odd-dimensional manifolds with boundary. Zbl 0920.58053Melrose, Richard B.; Piazza, Paolo 20 1997 Weyl’s conjecture for manifolds with concave boundary. Zbl 0436.58024Melrose, R. B. 20 1980 Index in \(K\)-theory for families of fibred cusp operators. Zbl 1126.58010Melrose, Richard; Rochon, Frédéric 20 2006 Spectral and scattering theory for symbolic potentials of order zero. Zbl 1038.35085Hassell, Andrew; Melrose, Richard; Vasy, András 20 2004 Analytic surgery and the eta invariant. Zbl 0838.57022Mazzeo, R. R.; Melrose, R. B. 20 1995 The index of projective families of elliptic operators. Zbl 1083.58021Mathai, Varghese; Melrose, Richard B.; Singer, Isadore M. 19 2005 Interaction of progressing waves for semilinear wave equations. II. Zbl 0653.35058Melrose, Richard B.; Ritter, Niles 18 1987 The Cauchy problem for effectively hyperbolic operators. Zbl 0544.35094Melrose, Richard 16 1983 Propagation of singularities for the wave equation on edge manifolds. Zbl 1147.58029Melrose, Richard; Vasy, András; Wunsch, Jared 16 2008 A mod \(k\) index theorem. Zbl 0760.58039Freed, Daniel S.; Melrose, Richard B. 16 1992 Contact degree and the index of Fourier integral operators. Zbl 0929.58012Epstein, Charles; Melrose, Richard 16 1998 Forward scattering by a convex obstacle. Zbl 0435.35066Melrose, R. B. 15 1980 Equivalence of glancing hypersurfaces. II. Zbl 0472.53045Melrose, R. B. 15 1981 Local Fourier-Airy integral operators. Zbl 0368.35054Melrose, Richard B. 14 1975 Polynomial bound on the distribution of poles in scattering by an obstacle. Zbl 0621.35073Melrose, Richard 14 1984 Analytic continuation and semiclassical resolvent estimates on asymptotically hyperbolic spaces. Zbl 1323.58020Melrose, Richard; Barreto, Antônio Sá; Vasy, András 14 2014 Microlocal propagation near radial points and scattering for symbolic potentials of order zero. Zbl 1152.35454Hassell, Andrew; Melrose, Richard; Vasy, András 13 2008 The radiation pattern of a diffracted wave near the shadow boundary. Zbl 0632.35056Melrose, Richard B.; Taylor, Michael E. 13 1986 The wave equation for a hypoelliptic operator with symplectic characteristics of codimension two. Zbl 0599.35139Melrose, Richard B. 12 1985 Fractional analytic index. Zbl 1115.58021Mathai, V.; Melrose, R. B.; Singer, I. M. 12 2006 The wave front set of the solution of a simple initial-boundary value problem with glancing rays. II. Zbl 0356.35056Friedlander, F. G.; Melrose, R. B. 10 1977 A cohomological invariant of discrete dynamical systems. Zbl 0482.58032Guillemin, Victor; Melrose, Richard 9 1981 A signature formula for manifolds with corners of codimension two. Zbl 0883.58038Hassell, Andrew; Mazzeo, Rafe; Melrose, Richard B. 9 1997 Airy operators. Zbl 0384.35052Melrose, R. B. 9 1978 Adiabatic limit, heat kernel and analytic torsion. Zbl 1318.58019Dai, Xianzhe; Melrose, Richard B. 9 2012 Generalized blow-up of corners and fiber products. Zbl 1372.57042Kottke, Chris; Melrose, Richard B. 9 2015 The trace of the wave group. Zbl 0547.35095Melrose, Richard 8 1984 Semi-linear diffraction of conormal waves. Zbl 0902.35004Melrose, Richard B.; Sá Barreto, Antônio; Zworski, Maciej 8 1996 An inverse spectral result for elliptical regions of \(\mathbb{R}^2\). Zbl 0415.35062Guillemin, Victor; Melrose, Richard 7 1979 Families index for pseudodifferential operators on manifolds with boundary. Zbl 1086.58011Melrose, Richard; Rochon, Frédéric 7 2004 The index of projective families of elliptic operators: the decomposable case. Zbl 1207.19006Mathai, Varghese; Melrose, Richard B.; Singer, Isadore M. 7 2009 Fredholm realizations of elliptic symbols on manifolds with boundary. Zbl 1161.58011Albin, Pierre; Melrose, Richard 6 2009 Normal self-intersections of the characteristic variety. Zbl 0336.35017Melrose, Richard B. 6 1975 Generalized backscattering and the Lax-Phillips transform. Zbl 1199.35270Melrose, R.; Uhlmann, G. 6 2008 Propagation for the wave group of a positive subelliptic second-order differential operator. Zbl 0696.35064Melrose, Richard 6 1986 Resolution of smooth group actions. Zbl 1218.58009Albin, Pierre; Melrose, Richard 6 2011 Fibrations, compactifications and algebras of pseudodifferential operators. Zbl 0853.35142Melrose, Richard B. 5 1996 Diffraction of singularities for the wave equation on manifolds with corners. Zbl 1277.35004Melrose, Richard; Vasy, András; Wunsch, Jared 5 2013 Differential boundary value problems of principal type. Zbl 0447.35053Melrose, R. B. 4 1979 Interaction of progressing waves through a nonlinear potential. Zbl 0554.35085Melrose, R. B. 4 1984 The Cauchy problem with polynomial growth conditions for partial differential operators with constant coefficients. Zbl 0337.35012Melrose, R. B. 4 1975 Loop-fusion cohomology and transgression. Zbl 1331.55002Kottke, Chris; Melrose, Richard B. 4 2015 Nonlinear interaction of a cusp and a plane. Zbl 0847.35086Melrose, Richard B.; Sá Barreto, Antônio 4 1995 Star products and local line bundles. Zbl 1061.47064Melrose, Richard 4 2004 Geometric optics and the bottom of the spectrum. Zbl 0889.35129Melrose, Richard B. 4 1997 Singularities of solutions to boundary value problems. Zbl 0452.35120Melrose, Richard B. 3 1980 Hypoelliptic operators with characteristic variety of codimension two and the wave equation. Zbl 0468.35032Melrose, R. B. 3 1980 Semilinear waves with cusp singularities. Zbl 0656.35098Melrose, Richard B. 3 1987 Propagation of singularities along gliding rays. Zbl 0358.35048Andersson, K. G.; Melrose, R. 3 1977 Singularities and the wave equation on conic spaces. Zbl 1122.58302Melrose, Richard B.; Wunsch, Jared 3 2001 Periodicity and the determinant bundle. Zbl 1130.58013Melrose, Richard; Rochon, Frédéric 3 2007 Resolution of the canonical fiber metrics for a Lefschetz fibration. Zbl 1404.30047Melrose, Richard; Zhu, Xuwen 3 2018 Geometry of pseudodifferential algebra bundles and Fourier integral operators. Zbl 1397.58015Mathai, Varghese; Melrose, Richard B. 3 2017 Relative Chern character, boundaries and index formulas. Zbl 1207.58020Albin, Pierre; Melrose, Richard 2 2009 The Cauchy problem and propagation of singularities. Zbl 0599.35095Melrose, Richard 2 1984 Periodic solutions of certain nonlinear autonomous wave equations. Zbl 0315.35007Melrose, Richard B.; Pemberton, Malcolm 2 1975 Conormality, cusps and nonlinear interaction. Zbl 0794.35005Melrose, Richard B. 2 1991 Scattering theory for strictly pseudoconvex domains. Zbl 0927.37034Melrose, Richard 2 1999 Eta forms and the odd pseudodifferential families index. Zbl 1239.58019Melrose, Richard; Rochon, Frédéric 2 2011 Transformation methods for boundary value problems. Zbl 0477.35087Melrose, Richard B. 1 1981 Elliptic boundary problems on spaces with conic points. Zbl 0481.35004Melrose, Richard B.; Mendoza, Gerardo A. 1 1981 Some spectrally isolated convex planar regions. Zbl 0504.53040Marvizi, Shahla; Melrose, Richard B. 1 1982 Homology and the Heisenberg algebra. Joint work with C. Epstein and G. Mendoza. Zbl 1054.58013Melrose, Richard 1 1997 Propagation de singularites pour des problèmes aux limites d’ordre 2. Zbl 0383.35043Melrose, R. B.; Sjöstrand, J. 1 1978 Boundaries, eta invariant and the determinant bundle. Zbl 1196.58015Melrose, Richard; Rochon, Frédéric 1 2008 Equivariant \(K\)-theory and resolution. I: Abelian actions. Zbl 07225720Dimakis, Panagiotis; Melrose, Richard 1 2020 Equivariant \(K\)-theory and resolution. I: Abelian actions. Zbl 07225720Dimakis, Panagiotis; Melrose, Richard 1 2020 Resolution of the canonical fiber metrics for a Lefschetz fibration. Zbl 1404.30047Melrose, Richard; Zhu, Xuwen 3 2018 Geometry of pseudodifferential algebra bundles and Fourier integral operators. Zbl 1397.58015Mathai, Varghese; Melrose, Richard B. 3 2017 Generalized blow-up of corners and fiber products. Zbl 1372.57042Kottke, Chris; Melrose, Richard B. 9 2015 Loop-fusion cohomology and transgression. Zbl 1331.55002Kottke, Chris; Melrose, Richard B. 4 2015 Asymptotics of solutions of the wave equation on de Sitter-Schwarzschild space. Zbl 1286.35145Melrose, Richard; Barreto, Antônio Sá; Vasy, András 27 2014 Analytic continuation and semiclassical resolvent estimates on asymptotically hyperbolic spaces. Zbl 1323.58020Melrose, Richard; Barreto, Antônio Sá; Vasy, András 14 2014 Diffraction of singularities for the wave equation on manifolds with corners. Zbl 1277.35004Melrose, Richard; Vasy, András; Wunsch, Jared 5 2013 Adiabatic limit, heat kernel and analytic torsion. Zbl 1318.58019Dai, Xianzhe; Melrose, Richard B. 9 2012 Resolution of smooth group actions. Zbl 1218.58009Albin, Pierre; Melrose, Richard 6 2011 Eta forms and the odd pseudodifferential families index. Zbl 1239.58019Melrose, Richard; Rochon, Frédéric 2 2011 Fredholm realizations of elliptic symbols on manifolds with boundary. II: Fibered boundary. Zbl 1217.58014Albin, Pierre; Melrose, Richard 1 2010 The index of projective families of elliptic operators: the decomposable case. Zbl 1207.19006Mathai, Varghese; Melrose, Richard B.; Singer, Isadore M. 7 2009 Fredholm realizations of elliptic symbols on manifolds with boundary. Zbl 1161.58011Albin, Pierre; Melrose, Richard 6 2009 Relative Chern character, boundaries and index formulas. Zbl 1207.58020Albin, Pierre; Melrose, Richard 2 2009 Propagation of singularities for the wave equation on edge manifolds. Zbl 1147.58029Melrose, Richard; Vasy, András; Wunsch, Jared 16 2008 Microlocal propagation near radial points and scattering for symbolic potentials of order zero. Zbl 1152.35454Hassell, Andrew; Melrose, Richard; Vasy, András 13 2008 Generalized backscattering and the Lax-Phillips transform. Zbl 1199.35270Melrose, R.; Uhlmann, G. 6 2008 Boundaries, eta invariant and the determinant bundle. Zbl 1196.58015Melrose, Richard; Rochon, Frédéric 1 2008 Periodicity and the determinant bundle. Zbl 1130.58013Melrose, Richard; Rochon, Frédéric 3 2007 Index in \(K\)-theory for families of fibred cusp operators. Zbl 1126.58010Melrose, Richard; Rochon, Frédéric 20 2006 Fractional analytic index. Zbl 1115.58021Mathai, V.; Melrose, R. B.; Singer, I. M. 12 2006 The index of projective families of elliptic operators. Zbl 1083.58021Mathai, Varghese; Melrose, Richard B.; Singer, Isadore M. 19 2005 Propagation of singularities for the wave equation on conic manifolds. Zbl 1088.58011Melrose, Richard; Wunsch, Jared 25 2004 Spectral and scattering theory for symbolic potentials of order zero. Zbl 1038.35085Hassell, Andrew; Melrose, Richard; Vasy, András 20 2004 Families index for pseudodifferential operators on manifolds with boundary. Zbl 1086.58011Melrose, Richard; Rochon, Frédéric 7 2004 Star products and local line bundles. Zbl 1061.47064Melrose, Richard 4 2004 Singularities and the wave equation on conic spaces. Zbl 1122.58302Melrose, Richard B.; Wunsch, Jared 3 2001 Scattering theory for strictly pseudoconvex domains. Zbl 0927.37034Melrose, Richard 2 1999 Pseudodifferential operators on manifolds with fibred boundaries. Zbl 1125.58304Mazzeo, Rafe; Melrose, Richard B. 68 1998 \(K\)-theory of \(C^*\)-algebras of b-pseudodifferential operators. Zbl 0898.46060Melrose, R.; Nistor, V. 30 1998 Contact degree and the index of Fourier integral operators. Zbl 0929.58012Epstein, Charles; Melrose, Richard 16 1998 Families of Dirac operators, boundaries and the \(B\)-calculus. Zbl 0955.58020Melrose, Richard B.; Piazza, Paolo 38 1997 An index theorem for families of Dirac operators on odd-dimensional manifolds with boundary. Zbl 0920.58053Melrose, Richard B.; Piazza, Paolo 20 1997 A signature formula for manifolds with corners of codimension two. Zbl 0883.58038Hassell, Andrew; Mazzeo, Rafe; Melrose, Richard B. 9 1997 Geometric optics and the bottom of the spectrum. Zbl 0889.35129Melrose, Richard B. 4 1997 Homology and the Heisenberg algebra. Joint work with C. Epstein and G. Mendoza. Zbl 1054.58013Melrose, Richard 1 1997 Scattering metrics and geodesic flow at infinity. Zbl 0855.58058Melrose, Richard; Zworski, Maciej 48 1996 Semi-linear diffraction of conormal waves. Zbl 0902.35004Melrose, Richard B.; Sá Barreto, Antônio; Zworski, Maciej 8 1996 Fibrations, compactifications and algebras of pseudodifferential operators. Zbl 0853.35142Melrose, Richard B. 5 1996 Geometric scattering theory. Zbl 0849.58071Melrose, Richard B. 164 1995 Analytic surgery and the accumulation of eigenvalues. Zbl 0854.58039Hassell, Andrew; Mazzeo, Rafe; Melrose, Richard B. 27 1995 The eta invariant and families of pseudodifferential operators. Zbl 0934.58025Melrose, Richard B. 26 1995 Analytic surgery and the eta invariant. Zbl 0838.57022Mazzeo, R. R.; Melrose, R. B. 20 1995 Nonlinear interaction of a cusp and a plane. Zbl 0847.35086Melrose, Richard B.; Sá Barreto, Antônio 4 1995 Spectral and scattering theory for the Laplacian on asymptotically Euclidean spaces. Zbl 0837.35107Melrose, Richard B. 116 1994 The Atiyah-Patodi-Singer index theorem. Zbl 0796.58050Melrose, Richard B. 319 1993 Calculus of conormal distributions on manifolds with corners. Zbl 0754.58035Melrose, Richard B. 84 1992 Analytic \(K\)-theory on manifolds with corners. Zbl 0761.55002Melrose, Richard B.; Piazza, Paolo 37 1992 A mod \(k\) index theorem. Zbl 0760.58039Freed, Daniel S.; Melrose, Richard B. 16 1992 Resolvent of the Laplacian on strictly pseudoconvex domains. Zbl 0758.32010Epstein, C. L.; Melrose, R. B.; Mendoza, G. A. 62 1991 Pseudodifferential operators, corners and singular limits. Zbl 0743.58033Melrose, Richard B. 28 1991 Conormality, cusps and nonlinear interaction. Zbl 0794.35005Melrose, Richard B. 2 1991 The adiabatic limit, Hodge cohomology and Leray’s spectral sequence for a fibration. Zbl 0702.58007Mazzeo, Rafe R.; Melrose, Richard B. 31 1990 Weyl asymptotics for the phase in obstacle scattering. Zbl 0686.35089Melrose, Richard B. 30 1988 Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature. Zbl 0636.58034Mazzeo, Rafe R.; Melrose, Richard B. 180 1987 Interaction of progressing waves for semilinear wave equations. II. Zbl 0653.35058Melrose, Richard B.; Ritter, Niles 18 1987 Semilinear waves with cusp singularities. Zbl 0656.35098Melrose, Richard B. 3 1987 The radiation pattern of a diffracted wave near the shadow boundary. Zbl 0632.35056Melrose, Richard B.; Taylor, Michael E. 13 1986 Propagation for the wave group of a positive subelliptic second-order differential operator. Zbl 0696.35064Melrose, Richard 6 1986 Near peak scattering and the corrected Kirchhoff approximation for a convex obstacle. Zbl 0591.58034Melrose, Richard B.; Taylor, Michael E. 71 1985 Interaction of nonlinear progressing waves for semilinear wave equations. Zbl 0575.35063Melrose, Richard; Ritter, Niles 53 1985 The wave equation for a hypoelliptic operator with symplectic characteristics of codimension two. Zbl 0599.35139Melrose, Richard B. 12 1985 Polynomial bound on the distribution of poles in scattering by an obstacle. Zbl 0621.35073Melrose, Richard 14 1984 The trace of the wave group. Zbl 0547.35095Melrose, Richard 8 1984 Interaction of progressing waves through a nonlinear potential. Zbl 0554.35085Melrose, R. B. 4 1984 The Cauchy problem and propagation of singularities. Zbl 0599.35095Melrose, Richard 2 1984 Polynomial bound on the number of scattering poles. Zbl 0535.35067Melrose, Richard 38 1983 The Cauchy problem for effectively hyperbolic operators. Zbl 0544.35094Melrose, Richard 16 1983 Singularities of boundary value problems. II. Zbl 0546.35083Melrose, R. B.; Sjöstrand, J. 72 1982 Boundary behaviour of the complex Monge-Ampère equation. Zbl 0496.35042Lee, John; Melrose, Richard 60 1982 Spectral invariants of convex planar regions. Zbl 0492.53033Marvizi, Shahla; Melrose, Richard 29 1982 Scattering theory and the trace of the wave group. Zbl 0525.47007Melrose, Richard 22 1982 Some spectrally isolated convex planar regions. Zbl 0504.53040Marvizi, Shahla; Melrose, Richard B. 1 1982 Transformation of boundary problems. Zbl 0492.58023Melrose, Richard B. 74 1981 Equivalence of glancing hypersurfaces. II. Zbl 0472.53045Melrose, R. B. 15 1981 A cohomological invariant of discrete dynamical systems. Zbl 0482.58032Guillemin, Victor; Melrose, Richard 9 1981 Transformation methods for boundary value problems. Zbl 0477.35087Melrose, Richard B. 1 1981 Elliptic boundary problems on spaces with conic points. Zbl 0481.35004Melrose, Richard B.; Mendoza, Gerardo A. 1 1981 Weyl’s conjecture for manifolds with concave boundary. Zbl 0436.58024Melrose, R. B. 20 1980 Forward scattering by a convex obstacle. Zbl 0435.35066Melrose, R. B. 15 1980 Singularities of solutions to boundary value problems. Zbl 0452.35120Melrose, Richard B. 3 1980 Hypoelliptic operators with characteristic variety of codimension two and the wave equation. Zbl 0468.35032Melrose, R. B. 3 1980 Lagrangian intersection and the Cauchy problem. Zbl 0396.58006Melrose, R. B.; Uhlmann, G. A. 72 1979 Singularities and energy decay in acoustical scattering. Zbl 0415.35050Melrose, R. B. 66 1979 The Poisson summation formula for manifolds with boundary. Zbl 0421.35082Guillemin, Victor; Melrose, Richard 40 1979 Microlocal structure of involutive conical refraction. Zbl 0422.58026Melrose, R. B.; Uhlmann, G. A. 24 1979 An inverse spectral result for elliptical regions of \(\mathbb{R}^2\). Zbl 0415.35062Guillemin, Victor; Melrose, Richard 7 1979 Differential boundary value problems of principal type. Zbl 0447.35053Melrose, R. B. 4 1979 Singularities of boundary value problems. I. Zbl 0368.35020Melrose, R. B.; Sjöstrand, J. 112 1978 Airy operators. Zbl 0384.35052Melrose, R. B. 9 1978 Propagation de singularites pour des problèmes aux limites d’ordre 2. Zbl 0383.35043Melrose, R. B.; Sjöstrand, J. 1 1978 The propagation of singularities along gliding rays. Zbl 0373.35053Andersson, K. G.; Melrose, R. B. 53 1977 The wave front set of the solution of a simple initial-boundary value problem with glancing rays. II. Zbl 0356.35056Friedlander, F. G.; Melrose, R. B. 10 1977 Propagation of singularities along gliding rays. Zbl 0358.35048Andersson, K. G.; Melrose, R. 3 1977 Equivalence of glancing hyper-surfaces. Zbl 0354.53033Melrose, R. B. 56 1976 Microlocal parametrices for diffractive boundary value problems. Zbl 0368.35055Melrose, Richard B. 48 1975 Local Fourier-Airy integral operators. Zbl 0368.35054Melrose, Richard B. 14 1975 Normal self-intersections of the characteristic variety. Zbl 0336.35017Melrose, Richard B. 6 1975 The Cauchy problem with polynomial growth conditions for partial differential operators with constant coefficients. Zbl 0337.35012Melrose, R. B. 4 1975 ...and 1 more Documents all cited Publications top 5 cited Publications 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 all top 5 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 all top 5 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) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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