Trace theorems for holomorphic semigroups and the second order Cauchy problem

El-Mennaoui, O.; Keyantuo, Valentin

doi:10.1090/s0002-9939-96-03133-4

Cited by 24 publications

(14 citation statements)

References 15 publications

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“…then we say that (T α (t)) t≥0 is a tempered α-times integrated cosine family in B(X) with generator A (see [14], for instance). Cosine families extend to R as even functions.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…since this is the value of α for ∆ to generate an integrated cosine family in L p (R N ), see [14,Proposition 3.2].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…It is implicitly contained in [14] and [24] altogether that a closed operator A generates a tempered integrated cosine function if and only if A is the infinitesimal generator of a bounded analytic semigroup on C + . In particular, and more precisely, if A is the generator of an α-times integrated cosine function…”

Section: Applications and Related Resultsmentioning

confidence: 99%

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Extension problem and fractional operators: semigroups and wave equations

2013

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Abstract. We extend results of Caffarelli-Silvestre and Stinga-Torrea regarding a characterization of fractional powers of differential operators via an extension problem. Our results apply to generators of integrated families of operators, in particular to infinitesimal generators of bounded C 0 semigroups and operators with purely imaginary symbol. We give integral representations to the extension problem in terms of solutions to the heat equation and the wave equation.

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“…then we say that (T α (t)) t≥0 is a tempered α-times integrated cosine family in B(X) with generator A (see [14], for instance). Cosine families extend to R as even functions.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…since this is the value of α for ∆ to generate an integrated cosine family in L p (R N ), see [14,Proposition 3.2].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

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Extension problem and fractional operators: semigroups and wave equations

2013

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“…We are not primarily concerned with studying new concepts in the theory of hypercyclicity and our main intention is, in fact, to analyze the basic properties of a new important class of abstract second order (ill-posed) PDEs (cf. [3], [23], [26], [32], [34]- [35], [39], [42]- [44], [49] and [56]- [57] for further information in this direction).…”

Section: Introductionmentioning

confidence: 99%

Hypercyclic and chaotic integrated C-cosine functions

Kostić

2012

Filomat

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The main purpose of the paper is to display the main structural properties of hypercyclic and chaotic integrated C-cosine functions. The notions of hypercyclicity, mixing and chaoticity of an ?-times integrated C-cosine function (??0) are defined by using distributional techniques. We provide several examples which justify our abstract theoretical approach.[Projekat Ministarstva nauke Republike Srbije, br. 144016]

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“…It is well known that the notion of integrated cosine functions for a positive integral number n was introduced by Arendt and Kellermann [2] in 1989. Then, the basic properties of exponentially bounded α-times integrated cosine functions (α ≥ 0) are investigated by many authors (cf., e.g., [4,6,19,21] and references therein). Strongly continuous integrated C-cosine functions which are not necessarily exponentially bounded are investigated in [18].…”

Section: Introductionmentioning

confidence: 99%