A SPECTRAL MULTIPLIER THEOREM FOR NON-SELF-ADJOINT OPERATORS

被引：1

作者：

Ouhabaz, El Maati ^{[1
]}

机构：

[1] Univ Bordeaux 1, CNRS, UMR 5251, Inst Math Bordeaux,Equipe Anal & Geometrie, F-33405 Talence, France

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2009年 / 361卷 / 12期

关键词：

LIE-GROUPS; FUNCTIONAL-CALCULUS; RIESZ MEANS; LP SPACES; KERNELS; SEMIGROUPS;

D O I：

10.1090/S0002-9947-09-04754-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a spectral multiplier theorem for non-self-adjoint operators. More precisely, we consider non-self-adjoint operators A : D(A) subset of L(2) -> L(2) having numerical range in a sector Sigma(w) of angle w, and whose heat kernel satisfies a Gaussian upper bound. We prove that for every bounded holomorphic function f on Sigma(w), f(A) acts on L(p) with L(p)-norm estimated by the behavior of a finite number of derivatives of f on the boundary of Sigma(w).

引用

页码：6567 / 6582

页数：16

共 50 条

[1] Spectral monodromy of non-self-adjoint operators
Quang Sang Phan
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 2014, 55 (01)
[2] SPECTRAL PROJECTORS OF A CLASS OF NON-SELF-ADJOINT OPERATORS
MURTAZIN, KK
[J]. MATHEMATICAL NOTES, 1984, 35 (3-4) : 213 - 218
[3] Spectral properties of random non-self-adjoint matrices and operators
Davies, EB
[J]. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2001, 457 (2005): : 191 - 206
[4] Spectral enclosures for non-self-adjoint extensions of symmetric operators
Behrndt, Jussi
Langer, Matthias
Lotoreichik, Vladimir
Rohleder, Jonathan
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2018, 275 (07) : 1808 - 1888
[5] Spectral Enclosures for Non-self-adjoint Discrete Schrodinger Operators
Ibrogimov, Orif O.
Stampach, Frantisek
[J]. INTEGRAL EQUATIONS AND OPERATOR THEORY, 2019, 91 (06)
[6] SPECTRAL RESOLUTIONS FOR NON-SELF-ADJOINT BLOCK CONVOLUTION OPERATORS
Zalot, Ewelina
[J]. OPUSCULA MATHEMATICA, 2022, 42 (03) : 459 - 487
[7] Spectral resolutions for non-self-adjoint block convolution operators
Zalot, Ewelina
[J]. arXiv, 2022,
[8] Spectral and Distribution of Eigenvalues of Non-self-adjoint Differential Operators
Alizadeh, Reza
Sameripour, Ali
[J]. SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, 2023, 47 (05) : 611 - 623
[9] Non-self-adjoint differential operators
Davies, EB
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2002, 34 : 513 - 532
[10] Non-self-adjoint operators and pseudospectra
Davies, E. B.
[J]. Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon's 60th Birthday: QUANTUM FIELD THEORY, STATISTICAL MECHANICS, AND NONRELATIVISTIC QUANTUM SYSTEMS, 2007, 76 : 141 - 151

← 1 2 3 4 5 →