Vector-valued Laplace Transforms and Cauchy Problems

2011 ◽  
Author(s):  
Wolfgang Arendt ◽  
Charles J.K. Batty ◽  
Matthias Hieber ◽  
Frank Neubrander
Keyword(s):  
Laplace Transforms ◽  
Cauchy Problems ◽  
Vector Valued

scholarly journals A Subordination Principle on Wright Functions and Regularized Resolvent Families

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Luciano Abadias ◽  
Pedro J. Miana
Keyword(s):  
Fractional Calculus ◽  
Lévy Processes ◽  
Levy Processes ◽  
Laplace Transforms ◽  
Cauchy Problems ◽  
Convolution Properties ◽  
Vector Valued ◽  
Resolvent Families

We obtain a vector-valued subordination principle forgα,gβ-regularized resolvent families which unified and improves various previous results in the literature. As a consequence, we establish new relations between solutions of different fractional Cauchy problems. To do that, we consider scaled Wright functions which are related to Mittag-Leffler functions, the fractional calculus, and stable Lévy processes. We study some interesting properties of these functions such as subordination (in the sense of Bochner), convolution properties, and their Laplace transforms. Finally we present some examples where we apply these results.

Vector-valued Laplace Transforms and Cauchy Problems

2001 ◽  
Author(s):  
Wolfgang Arendt ◽  
Charles J. K. Batty ◽  
Matthias Hieber ◽  
Frank Neubrander
Keyword(s):  
Laplace Transforms ◽  
Cauchy Problems ◽  
Vector Valued

Some vector-valued laplace transforms

1973 ◽  
Vol 16 (1) ◽  
pp. 73-86
Author(s):  
D. Leviatan
Keyword(s):  
Laplace Transforms ◽  
Vector Valued

scholarly journals FINITE AND LOCAL LAPLACE TRANSFORMS IN BANACH SPACES

2003 ◽  
Vol 46 (2) ◽  
pp. 357-372 ◽  
Author(s):  
Valentin Keyantuo ◽  
Claus Müller ◽  
Peter Vieten
Keyword(s):  
Banach Spaces ◽  
Laplace Transforms ◽  
Subject Classification ◽  
Primary 44A10 ◽  
Classic Approach ◽  
Vector Valued

AbstractWe establish two characterizations of local Laplace transforms in Banach spaces. The first result follows the classic approach of Widder, while the second is in terms of vector-valued moment sequences. As a consequence, we derive characterizations of nilpotent semigroups.AMS 2000 Mathematics subject classification: Primary 44A10; 47D03

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