Resolvent characterisation of generators of cosine functions and \(C_0\)-groups

DOI10.1007/s00028-013-0178-2zbMath1287.47035OpenAlexW2017430922WikidataQ59303099 ScholiaQ59303099MaRDI QIDQ358608

Sebastian Król

Publication date: 9 August 2013

Published in: Journal of Evolution Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00028-013-0178-2

zbMATH Keywords

cosine functionfunctional calculusgrowth bound\(C_0\)-groupFattorini's theoremGearhart's theoremsquare root reduction

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Operator sine and cosine functions and higher-order Cauchy problems (47D09)

Related Items (5)

Abel ergodic theorems for strongly continuous cosine operators ⋮ Growth bounds for \(\alpha \)-times resolvent families ⋮ Characterizations of domains of fractional powers for non-negative operators ⋮ Remarks on a Characterization of Generators of Bounded $$C_0$$-Semigroups ⋮ A Besov algebra calculus for generators of operator semigroups and related norm-estimates

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Differential equations in Banach spaces. II: Theory of cosine operator functions
• Convex domains and K-spectral sets
• Vector-valued cosine transforms
• A transference principle for general groups and functional calculus on UMD spaces
• Numerical range and functional calculus in Hilbert space
• The group reduction for bounded cosine functions on UMD spaces
• Operators similar to unitary of selfadjoint ones
• On the inverse Laplace transform for \(C_0\)-semigroups in UMD-spaces
• Carleson curves, Muckenhoupt weights, and Toeplitz operators
• A perturbation theorem for operator semigroups in Hilbert spaces
• On the inversion of the Laplace transform for resolvent families in \(UMD\) spaces
• Some estimates for analytic functions of strip or sectorial operators
• Spectral properties of operator logarithms
• Conditions on the generator of a uniformly bounded \(C_0\)-semigroup
• Characteristic conditions of the generation of \(C_0\) semigroups in a Hilbert space
• A skew normal dilation on the numerical range of an operator
• A characterization of group generators on Hilbert spaces and the \(H^\infty\) -calculus
• Operators with numerical range in a parabola
• Operators with numerical range in a conic domain
• Functional calculus for groups and applications to evolution equations
• The functional calculus for sectorial operators
• Ordinary differential equations in linear topological spaces. I
• Ordinary differential equations in linear topological space. II
• On a perturbation theorem of Kaiser and Weis
• THE COMPLEX INVERSION FORMULA REVISITED
• On the growth of solutions to second order differential equations in Banach spaces
• A Characterization of Strongly Continuous Groups of Linear Operators on a Hilbert Space
• On the Theory of Fourier Transforms
• On group decompositions of bounded cosine sequences
• $H^\infty $ calculus and dilatations
• On the invertibility and bounded extension of \(C_0\)-semigroups
• On operator cosine functions in UMD spaces

This page was built for publication: Resolvent characterisation of generators of cosine functions and \(C_0\)-groups