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- Richard B. Melrose

Discipline name
D-index
D-index (Discipline H-index) only includes papers and citation values for an examined
discipline in contrast to General H-index which accounts for publications across all
disciplines.
Citations
Publications
World Ranking
National Ranking

Mathematics
D-index
44
Citations
8,949
113
World Ranking
1077
National Ranking
509

1992 - Fellow of John Simon Guggenheim Memorial Foundation

1986 - Fellow of the American Academy of Arts and Sciences

- Mathematical analysis
- Geometry
- Pure mathematics

Mathematical analysis, Laplace operator, Pure mathematics, Boundary value problem and Scattering theory are his primary areas of study. Mathematical analysis is often connected to Dirac in his work. His Laplace operator research includes themes of Manifold and Resolvent.

His Manifold study incorporates themes from Vector field, Cusp, Spectrum and Lie algebra. The study incorporates disciplines such as Equivalence, Calculus and Dirac spinor in addition to Pure mathematics. His research in Scattering theory focuses on subjects like Scattering amplitude, which are connected to Scattering length, Inverse scattering problem and Inverse scattering transform.

- The Atiyah-Patodi-Singer Index Theorem (855 citations)
- Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature (479 citations)
- Geometric scattering theory (401 citations)

Richard B. Melrose mainly focuses on Mathematical analysis, Pure mathematics, Manifold, Boundary value problem and Wave equation. His study in the field of Laplace operator, Gravitational singularity and Metric also crosses realms of Scattering theory and Diffraction. The various areas that Richard B. Melrose examines in his Laplace operator study include Vector field, Spectrum and Resolvent.

He has researched Scattering theory in several fields, including Scattering amplitude and Scattering length. Richard B. Melrose has included themes like Space and Fiber in his Manifold study. His work on Mixed boundary condition and Free boundary problem as part of general Boundary value problem study is frequently connected to Singular boundary method, therefore bridging the gap between diverse disciplines of science and establishing a new relationship between them.

- Mathematical analysis (55.73%)
- Pure mathematics (47.33%)
- Manifold (22.90%)

- Pure mathematics (47.33%)
- Mathematical analysis (55.73%)
- Manifold (22.90%)

Richard B. Melrose mostly deals with Pure mathematics, Mathematical analysis, Manifold, Fiber and Compactification. His study in Pure mathematics is interdisciplinary in nature, drawing from both Resolution and Iterated function. Richard B. Melrose performs multidisciplinary study on Mathematical analysis and Semiclassical physics in his works.

Smooth structure, Domain and Transversality is closely connected to Space in his research, which is encompassed under the umbrella topic of Manifold. His work carried out in the field of Compactification brings together such families of science as Conjugacy class and Schwartz space. His work deals with themes such as Surface, Conformal map, Wave front set and Laplace operator, which intersect with Metric.

- Spectral and Scattering Theory for the Laplacian on Asymptotically Euclidian Spaces (223 citations)
- Asymptotics of Solutions of the Wave Equation on de Sitter-Schwarzschild Space (66 citations)
- Analytic Continuation and Semiclassical Resolvent Estimates on Asymptotically Hyperbolic Spaces (37 citations)

- Mathematical analysis
- Geometry
- Algebra

The scientist’s investigation covers issues in Mathematical analysis, Manifold, Riemann hypothesis, Metric and Wave equation. His studies link Anti-de Sitter space with Mathematical analysis. His Manifold research incorporates elements of Space, Transversality, Fundamental solution and Domain.

His Riemann hypothesis study combines topics in areas such as Surface, Conformal map, Wave front set and Laplace operator. The Metric study combines topics in areas such as Compactification and Moduli space. The study incorporates disciplines such as Hyperbolic partial differential equation, Gravitational singularity and Cauchy surface in addition to Wave equation.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

The Atiyah-Patodi-Singer Index Theorem

Richard B. Melrose.

**(1993)**

1415 Citations

The Atiyah-Patodi-Singer Index Theorem

Richard B. Melrose.

**(1993)**

1415 Citations

Geometric scattering theory

Richard B. Melrose.

**(1995)**

635 Citations

Geometric scattering theory

Richard B. Melrose.

**(1995)**

635 Citations

Singularities of boundary value problems. I

R. B. Melrose;J. Sjöstrand.

Communications on Pure and Applied Mathematics **(1978)**

517 Citations

Singularities of boundary value problems. I

R. B. Melrose;J. Sjöstrand.

Communications on Pure and Applied Mathematics **(1978)**

517 Citations

Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature

Rafe R Mazzeo;Richard B Melrose.

Journal of Functional Analysis **(1987)**

513 Citations

Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature

Rafe R Mazzeo;Richard B Melrose.

Journal of Functional Analysis **(1987)**

513 Citations

Spectral and Scattering Theory for the Laplacian on Asymptotically Euclidian Spaces

Richard B. Melrose.

**(2020)**

346 Citations

Spectral and Scattering Theory for the Laplacian on Asymptotically Euclidian Spaces

Richard B. Melrose.

**(2020)**

346 Citations

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