Complex powers of elliptic pseudodifferential operators

verfasst von

Elmar Schrohe

Abstract

The aim of this paper is the construction of complex powers of elliptic pseudodifferential operators and the study of the analytic properties of the corresponding kernels k_S (x,y). For x=y, the case of principal interest, the domain of holomorphy and the singularities of k_S (x,x) are shown to depend on the asymptotic expansion of the symbol. For classical symbols, k_S (x,x) is known to be meromorphic on ℂ with simple poles in a set of equidistant points on the real axis. In the more general cases considered here, the singularities may be distributed over a half plane and k_S (x,x) can not always be extended to 337-2. An example is given where k_S (x,x) has a vertical line as natural boundary.

Externe Organisation(en)

Johannes Gutenberg-Universität Mainz

Typ

Artikel

Journal

Integral Equations and Operator Theory

Band

9

Seiten

337-354

Anzahl der Seiten

18

ISSN

0378-620X

Publikationsdatum

05.1986

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Analysis, Algebra und Zahlentheorie

Elektronische Version(en)

https://doi.org/10.1007/BF01199350 (Zugang: Geschlossen)