Stieltjes transforms defined by C0-semigroups
نویسنده
چکیده
In this paper we use the resolvent semigroup associated to a C0semigroup to introduce the vector-valued Stieltjes transform defined by a C0-semigroup. We give new results which extend known ones in the case of scalar generalized Stieltjes transform. We work with the vector-valued Weyl fractional calculus to present a deep connection between both concepts. Mathematics Subject Classification (2000). 26A33, 44A10, 47D06.
منابع مشابه
The Restricted Algebras on Inverse Semigroups Iii, Fourier Algebra
The Fourier and Fourier-Stieltjes algebras A(G) and B(G) of a locally compact group G are introduced and studied in 60’s by Piere Eymard in his PhD thesis. If G is a locally compact abelian group, then A(G) ≃ L(Ĝ), and B(G) ≃ M(Ĝ), via the Fourier and Fourier-Stieltjes transforms, where Ĝ is the Pontryagin dual of G. Recently these algebras are defined on a (topological or measured) groupoid an...
متن کاملOn powers of Stieltjes moment sequences, II
We consider the set of Stieltjes moment sequences, for which every positive power is again a Stieltjes moment sequence, we and prove an integral representation of the logarithm of the moment sequence in analogy to the Lévy-Khintchine representation. We use the result to construct product convolution semigroups with moments of all orders and to calculate their Mellin transforms. As an applicatio...
متن کاملThe approximation of Laplace-Stieltjes transforms with finite order
In this paper, we study the irregular growth of an entire function defined by the Laplace-Stieltjes transform of finite order convergent in the whole complex plane and obtain some results about λ-lower type. In addition, we also investigate the problem on the error in approximating entire functions defined by the Laplace-Stieltjes transforms. Some results about the irregular growth, the error, ...
متن کامل2 Generalized Cauchy - Stieltjes Transforms and Markov Transforms
We express the generalized Cauchy-Stieltjes transforms of some particular Beta distributions depending on a positive parameter λ as λ-powered Cauchy-Stieltjes transforms of some probability measures. The Cauchy-Stieltjes transforms of the latter measures are shown to be the geometric mean of the Cauchy-Stieltjes transform of the Wigner law together with another one. Moreover, they are absolutel...
متن کاملOn the Lp-theory of C0-semigroups associated with second order elliptic operators. II
We study positive C0-semigroups on Lp associated with second order uniformly elliptic divergence type operators with singular lower order terms, subject to a wide class of boundary conditions. We obtain an interval (pmin, pmax) in the Lp-scale where these semigroups can be defined, including the case 2 6∈ (pmin, pmax). We present an example showing that the result is optimal. We also show that ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Computational Applied Mathematics
دوره 234 شماره
صفحات -
تاریخ انتشار 2010