Global Hypoellipticity and spectral theory
著者
書誌事項
Global Hypoellipticity and spectral theory
（Mathematical research = Mathematische Forschung, v. 92）
Akademie, 1996
大学図書館所蔵 全7件
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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