On the Laplace transform for vector valued hyperfunctions

Vector-valued Laplace Transforms and Cauchy Problems

This monograph gives a systematic account of the theory of vector-valued Laplace transforms, ranging from representation theory to Tauberian theorems. In parallel, the theory of linear Cauchy problems and semigroups of operators is developed completely in the spirit of Laplace transforms. Existence and uniqueness, regularity, approximation and above all asymptotic behaviour of solutions are stu...

On the Vector Valued Fourier Transform and Compatibility of Operators*

is the dual group of G, and p ′ the conjugate exponent of p. An operator T between Banach spaces X and Y is said to be compatible with the Fourier transform F G if F G ⊗ T : Lp(G)⊗X → Lp′ (G ′ )⊗ Y admits a continuous extension [F , T ] : [Lp(G), X ] → [Lp′ (G ′ ), Y ]. We show that if G is topologically isomorphic with R×Z×F, where l and m are nonnegative integers and F is a compact group with...

Laplace Transform of Distribution-valued Functions and Its Applications

1. Notation and notions We repeat some definitions and facts, we need in our exposition but for special case. Let Q be an open set belonging to Rn. By D(Q) we denote the space {φ ∈ C∞(Q); suppφ ⊂ Kφ}, Kφ is a compact set in Q which depends on φ. D′(Q) is the space of continuous linear functionals on D(Q) the space of distributions. Every f ∈ Lloc(Q) defines a distribution, called regular distri...

On the Laplace transform decomposition algorithm for solving nonlinear differential equations

On the character space of Banach vector-valued function algebras

‎Given a compact space $X$ and a commutative Banach algebra‎ ‎$A$‎, ‎the character spaces of $A$-valued function algebras on $X$ are‎ ‎investigated‎. ‎The class of natural $A$-valued function algebras‎, ‎those whose characters can be described by means of characters of $A$ and‎ ‎point evaluation homomorphisms‎, ‎is introduced and studied‎. ‎For an‎ ‎admissible Banach $A$-valued function algebra...