( $$ L^p, L^q $$ )-Admissibility and Exponential Dichotomy of Evolutionary Processes on the Half-line

Preda, Petre; Pogan, Alin; Preda, Ciprian

doi:10.1007/s00020-002-1268-7

Cited by 40 publications

(38 citation statements)

References 16 publications

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“…In 2001 Minh and Huy considered the integral equation (E U ) on L p -spaces and obtained the equivalence (i)⇔(iv) in [17]. A different dichotomy concept is characterized by Preda, Pogan and Preda in [19], under the assumption that there exists a dichotomy projection family compatible with U (see (i)⇔(v)). An approach which generalizes the above equivalences (see (i)⇔(vi)) was given in [25], treating both discrete and integral case.…”

Section: Introductionmentioning

confidence: 99%

Integral Equations on Function Spaces and Dichotomy on the Real Line

Sasu

2006

Integr. equ. oper. theory

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The purpose of this paper is to give new and general characterizations for uniform dichotomy and uniform exponential dichotomy of evolution families on the real line. We consider two general classes denoted T (R) and H(R) and we prove that if V, W are Banach function spaces with V ∈ T (R) and W ∈ H(R), then the admissibility of the pair (W (R, X), V (R, X)) for an evolution family U = {U (t, s)} t≥s implies the uniform dichotomy of U. In addition, we consider a subclass W(R) ⊂ H(R) and we prove that if W ∈ W(R), then the admissibility of the pair (W (R, X), V (R, X)) implies the uniform exponential dichotomy of the family U. This condition becomes necessary if V ⊂ W . Finally, we present some applications of the main results. Mathematics Subject Classification (2000). Primary 34D09; Secondary 34D05.

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Section: Introductionmentioning

confidence: 99%

Integral Equations on Function Spaces and Dichotomy on the Real Line

Sasu

2006

Integr. equ. oper. theory

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“…Also using a discrete time argument, an extension of the well-known Datko's result [3] was obtained in [13].…”

Section: Introductionmentioning

confidence: 85%

Functionals on function and sequence spaces connected with the exponential stability of evolutionary processes

Preda¹,

Pogan²,

Preda³

2006

Czech Math J

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“…For more recent results devoted to continuous and discrete evolution families, we refer to [5][6][7][8][9][10][11][12][13][14][15] for those dealing with uniform exponential behaviour and to [16][17][18][19][20] for those that consider various concepts of nonuniform exponential behaviour.…”

Section: Introductionmentioning

confidence: 99%