What is he best known for?
The fields of study he is best known for:
- 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.
His most cited work include:
- 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)
What are the main themes of his work throughout his whole career to date?
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.
He most often published in these fields:
- Mathematical analysis (55.73%)
- Pure mathematics (47.33%)
- Manifold (22.90%)
What were the highlights of his more recent work (between 2010-2020)?
- Pure mathematics (47.33%)
- Mathematical analysis (55.73%)
- Manifold (22.90%)
In recent papers he was focusing on the following fields of study:
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.
Between 2010 and 2020, his most popular works were:
- 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)
In his most recent research, the most cited papers focused on:
- 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.
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