Global Hypoellipticity and spectral theory
著者
書誌事項
Global Hypoellipticity and spectral theory
（Mathematical research = Mathematische Forschung, v. 92）
Akademie, 1996
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内容説明・目次
内容説明
This volume looks at the spectral theory of global hypoelliptic pseudodifferential operators in Rn and the asymptotic estimate of the eigenvalue distribution function N of a hypoelliptic differential operator with polynomial coefficients in Rn. The first section introduces the pseudodifferential calculus with respect to a multi-quasi-elliptic weight; while the second part computes the asymptotic expansion of N for a multi-quasi-elliptic differential operator with polynomial coefficients. This is achieved by computing the asymptotic expansion of the Weyl term V. In this way, results are obtained with respect to a refinement of the asymptotic formula and the class of symbols considered.
目次
- Pseudodifferential Operators in Rn: Multiquasi-Elliptic Polynomials, Related Sobolev Spaces and Classes of Pseudodifferential Operators, Related Fourier Integral Operators
- Spectral Theory: The Spectrum of the Self-Adjoint Multi-Quasi-Elliptic Operators, Asymptotics for Weyl Integrals of Multi-Quasi-Elliptic Polynomials, Sharp Remainder for the Counting Function
- Other Applications: A Class of Vector Valued Pseudodifferential Operators, Hypoelliptic Degenerate Equations of Grushin Type, Wave Front Sets in the Multi-Quasielliptic Case, Some Boundary Value Problems in Unbounded Domains of Rn.
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