Displaying similar documents to “On an integral transform by R. S. Phillips”

The index 2 F 1 -transform of generalized functions

N. Hayek, Benito J. González (1993)

Commentationes Mathematicae Universitatis Carolinae

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In this paper the index transformation F ( τ ) = ∫ 0 ∞ f ( t ) 2 F 1 ( μ + 1 2 + i τ , μ + 1 2 - i τ ; μ + 1 ; - t ) t α d t 2 F 1 ( μ + 1 2 + i τ , μ + 1 2 - i τ ; μ + 1 ; - t ) being the Gauss hypergeometric function, is defined on certain space of generalized functions and its inversion formula established for distributions of compact support on 𝐈 = ( 0 , ∞ ) .

Unbounded well-bounded operators, strongly continuous semigroups and the Laplace transform

Ralph deLaubenfels (1992)

Studia Mathematica

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Suppose A is a (possibly unbounded) linear operator on a Banach space. We show that the following are equivalent. (1) A is well-bounded on [0,∞). (2) -A generates a strongly continuous semigroup e - s A s ≤ 0 such that ( 1 / s 2 ) e - s A s > 0 is the Laplace transform of a Lipschitz continuous family of operators that vanishes at 0. (3) -A generates a strongly continuous differentiable semigroup e - s A s ≥ 0 and ∃ M < ∞ such that ∥ H n ( s ) ∥ ≡ ∥ ( ∑ k = 0 n ( s k A k ) / k ! ) e - s A ∥ ≤ M , ∀s > 0, n ∈ ℕ ∪ 0. (4) -A generates a strongly continuous holomorphic semigroup e - z A R e ( z ) > 0 that is O(|z|)...