A perturbation theorem for operator semigroups in Hilbert spaces

2003 ◽  
Vol 67 (1) ◽  
pp. 63-75 ◽  
Author(s):  
C. Kaiser ◽  
L. Weis
Keyword(s):  
Hilbert Spaces ◽  
Operator Semigroups ◽  
Perturbation Theorem

scholarly journals A Besov algebra calculus for generators of operator semigroups and related norm-estimates

2019 ◽  
Author(s):  
Charles Batty ◽  
Alexander Gomilko ◽  
Yuri Tomilov
Keyword(s):  
Banach Spaces ◽  
Hilbert Spaces ◽  
Functional Calculus ◽  
The Other ◽  
Direct Approach ◽  
Operator Semigroups ◽  
Holomorphic Semigroups ◽  
Norm Estimates ◽  
Strict Extension ◽  
Bounded Holomorphic

Abstract We construct a new bounded functional calculus for the generators of bounded semigroups on Hilbert spaces and generators of bounded holomorphic semigroups on Banach spaces. The calculus is a natural (and strict) extension of the classical Hille–Phillips functional calculus, and it is compatible with the other well-known functional calculi. It satisfies the standard properties of functional calculi, provides a unified and direct approach to a number of norm-estimates in the literature, and allows improvements of some of them.

scholarly journals Refined scales of decaying rates of operator semigroups on Hilbert spaces: Typical behavior

2020 ◽  
Vol 148 (6) ◽  
pp. 2509-2523
Author(s):  
Moacir Aloisio ◽  
Silas L. Carvalho ◽  
César R. de Oliveira
Keyword(s):  
Hilbert Spaces ◽  
Operator Semigroups

scholarly journals Optimal rates of decay for operator semigroups on Hilbert spaces

2019 ◽  
Vol 346 ◽  
pp. 359-388 ◽  
Author(s):  
Jan Rozendaal ◽  
David Seifert ◽  
Reinhard Stahn
Keyword(s):  
Hilbert Spaces ◽  
Operator Semigroups ◽  
Rates Of Decay

Unbounded Linear Operators

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Von Neumann ◽  
Limit Circle ◽  
Sectorial Operators ◽  
Closed Operators ◽  
The Stability ◽  
Symmetric Operators ◽  
Unbounded Linear Operators ◽  
Special Case

This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.

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