Boundary value problems, Schrödinger operators, deformation quantization
著者
書誌事項
Boundary value problems, Schrödinger operators, deformation quantization
（Mathematical topics, v. 8 . Advances in partial differential equations）
Akademie Verlag, c1995
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注記
Includes bibliographical references
内容説明・目次
内容説明
The analysis of boundary value problems has a long tradition in mathematics. Understanding the criteria for solvability and the structure of the solutions is of central interest both for the theory and applications. Boundary value problems on manifolds with singularities present an additional challenge. They exhibit a wealth of analytic and algebraic structures, also under the aspect of index theory. In the first contribution to this volume, boundary value problems without the transmission condition are interpreted as particular problems on manifolds with edges; the paper deals with the new effects caused by variable and branching asymptotics. In the second paper, a pseudo-differential calculus is constructed for boundary value problems on manifolds with conical singularities. A concept of ellipticity is introduced that allows a parametrix construction and entails the Fredholm property in weighted Sobolev spaces. Moreover, this approach lays the foundations for treating boundary value problems on manifolds with edges. Two further contributions deals with deformation quantization, an important topic of mathematical physics.
The first one gives a complete proof of the index theorem in deformation quantization, while the other one treats trace densities. The final article in this volume, also from the area of mathematical physics, presents new results on the spectrum of perturbed periodic Schrodinger operators.
目次
- The Variable Discrete Asyptotics in Pseudo-Differential Boundary Value Problems
- Boundary Value Problems in Boutet de Monvel's Algebra for Manifolds with Conical Singularities
- The Index Theorem for Deformation Quantization
- A Trace Density in Deformation Quantization
- The Discrete Spectrum in Gaps of the Perturbed Periodic Shrvdinger Operator.
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