Bounds and Stieltjes transform representations for positive real functions
نویسندگان
چکیده
منابع مشابه
The Representations and Positive Type Functions of Some Homogenous Spaces
‎For a homogeneous spaces ‎$‎G/H‎$‎, we show that the convolution on $L^1(G/H)$ is the same as convolution on $L^1(K)$, where $G$ is semidirect product of a closed subgroup $H$ and a normal subgroup $K $ of ‎$‎G‎$‎. ‎Also we prove that there exists a one to one correspondence between nondegenerat $ast$-representations of $L^1(G/H)$ and representations of ...
متن کاملStieltjes and other integral representations for functions of Lambert W
where lnk z = ln z+2πik, and ln z is the principal branch of natural logarithm [14]. This paper considers only the principal branch k = 0, which is the branch that maps the positive real axis onto itself, and therefore we shall usually abbreviate W0 as W herein. Many functions of W are members of a number of function classes, specifically, the classes of Stieltjes functions, Pick functions and ...
متن کاملReal-variables characterization of generalized Stieltjes functions
We obtain a characterization of generalized Stieltjes functions of any order λ > 0 in terms of inequalities for their derivatives on (0,∞). When λ = 1, this provides a new and simple proof of a characterization of Stieltjes functions first obtained by Widder in 1938.
متن کاملThe Iterated Stieltjes Transform.
THEOREM 4. If Q is a Lie algebra of type All then n > 2 and $ SJ' where J is an i.a.a. of second kind in a simple algebra [. Thus a complete classification of Lie algebras of type A,, depends on the classification of simple associative algebras of second kind and of i.a.a.'s relative to cogredience in these algebras. It can be shown that the latter problem is essentially one of ordinary cogredi...
متن کاملExtending the Stieltjes Transform
The classical Stieltjes transform is extended to a subspace of Boehmians. The transform is shown to be an analytic function in the half-plane Re z > 0. Some Abelian type theorems are established.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1961
ISSN: 0022-247X
DOI: 10.1016/0022-247x(61)90078-6