Details
| Original language | English |
|---|---|
| Pages (from-to) | 337-354 |
| Number of pages | 18 |
| Journal | Integral Equations and Operator Theory |
| Volume | 9 |
| Issue number | 3 |
| Publication status | Published - May 1986 |
| Externally published | Yes |
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 kS (x,y). For x=y, the case of principal interest, the domain of holomorphy and the singularities of kS (x,x) are shown to depend on the asymptotic expansion of the symbol. For classical symbols, kS (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 kS (x,x) can not always be extended to 337-2. An example is given where kS (x,x) has a vertical line as natural boundary.
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Algebra and Number Theory
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In: Integral Equations and Operator Theory, Vol. 9, No. 3, 05.1986, p. 337-354.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Complex powers of elliptic pseudodifferential operators
AU - Schrohe, Elmar
N1 - Copyright: Copyright 2007 Elsevier B.V., All rights reserved.
PY - 1986/5
Y1 - 1986/5
N2 - 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 kS (x,y). For x=y, the case of principal interest, the domain of holomorphy and the singularities of kS (x,x) are shown to depend on the asymptotic expansion of the symbol. For classical symbols, kS (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 kS (x,x) can not always be extended to 337-2. An example is given where kS (x,x) has a vertical line as natural boundary.
AB - 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 kS (x,y). For x=y, the case of principal interest, the domain of holomorphy and the singularities of kS (x,x) are shown to depend on the asymptotic expansion of the symbol. For classical symbols, kS (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 kS (x,x) can not always be extended to 337-2. An example is given where kS (x,x) has a vertical line as natural boundary.
UR - http://www.scopus.com/inward/record.url?scp=0041504597&partnerID=8YFLogxK
U2 - 10.1007/BF01199350
DO - 10.1007/BF01199350
M3 - Article
AN - SCOPUS:0041504597
VL - 9
SP - 337
EP - 354
JO - Integral Equations and Operator Theory
JF - Integral Equations and Operator Theory
SN - 0378-620X
IS - 3
ER -