scholarly journals Necessary and sufficient conditions for the validity of Hilbert type integral inequalities with a class of quasi-homogeneous kernels and its application in operator theory

2018 ◽  
pp. 777-788 ◽  
Author(s):  
Yong Hong ◽  
Bing He ◽  
Bicheng Yang
Keyword(s):  
Operator Theory ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Integral Inequalities ◽  
Type Integral ◽  
Necessary And Sufficient ◽  
Hilbert Type

scholarly journals The Zak Transform on Gelfand–Shilov and Modulation Spaces with Applications to Operator Theory

2020 ◽  
Vol 15 (1) ◽  
Author(s):  
Joachim Toft
Keyword(s):  
Operator Theory ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Operators ◽  
Modulation Spaces ◽  
Zak Transform ◽  
Periodic Functions ◽  
Distribution Spaces ◽  
Necessary And Sufficient

AbstractWe characterize Gelfand–Shilov spaces, their distribution spaces and modulation spaces in terms of estimates of their Zak transforms. We use these results for general investigations of quasi-periodic functions and distributions. We also establish necessary and sufficient conditions for linear operators in order for these operators should be conjugations by Zak transforms.

scholarly journals H-function with complex parameters I: existence

2001 ◽  
Vol 25 (9) ◽  
pp. 571-586
Author(s):  
Fadhel A. Al-Musallam ◽  
Vu Kim Tuan
Keyword(s):  
Sufficient Conditions ◽  
Integral Transforms ◽  
Necessary And Sufficient Conditions ◽  
Special Cases ◽  
Type Integral ◽  
Necessary And Sufficient

AnH-function with complex parameters is defined by a Mellin-Barnes type integral. Necessary and sufficient conditions under which the integral defining theH-function converges absolutely are established. Some properties, special cases, and an application to integral transforms are given.

scholarly journals Necessary and sufficient conditions on weighted multilinear fractional integral inequality

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Zhou Yongliang ◽  
Deng Yangkendi ◽  
Wu Di ◽  
Yan Dunyan
Keyword(s):  
Integral Inequality ◽  
Sobolev Inequality ◽  
Fractional Integral ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Integral Inequalities ◽  
Multilinear Fractional Integral ◽  
Sufficient And Necessary Conditions ◽  
Necessary And Sufficient

<p style='text-indent:20px;'>We consider certain kinds of weighted multi-linear fractional integral inequalities which can be regarded as extensions of the Hardy-Littlewood-Sobolev inequality. For a particular case, we characterize the sufficient and necessary conditions which ensure that the corresponding inequality holds. For the general case, we give some sufficient conditions and necessary conditions, respectively.</p>

scholarly journals Necessary and sufficient conditions for the existence of a generalized Stieltjes integral

1978 ◽  
Vol 26 (4) ◽  
pp. 501-510 ◽  
Author(s):  
A. M. Russell
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sufficient Condition ◽  
Stieltjes Integral ◽  
Convexity Condition ◽  
Necessary And Sufficient Condition ◽  
Type Integral ◽  
Necessary And Sufficient ◽  
Stieltjes Type

AbstractIn Russell (1973) a Riemann-type necessary and sufficient condition was given for the existence of (defined also in Russell (1975)) when f was bounded and g was k-convex in [a′, b′]. In this paper we present necessary and sufficient conditions for the existence of a particular Stieltjes-type integral without imposing a convexity condition upon g. These conditions are used to obtain an additivity result for the integral over adjoining intervals without any additional restrictions being imposed upon the functions involved.

scholarly journals Subnormality of Powers of Multivariable Weighted Shifts

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Sang Hoon Lee ◽  
Woo Young Lee ◽  
Jasang Yoon
Keyword(s):  
Hilbert Space ◽  
Open Problem ◽  
Operator Theory ◽  
Sufficient Conditions ◽  
Weighted Shift ◽  
Necessary And Sufficient Conditions ◽  
Weighted Shifts ◽  
Hilbert Space Operators ◽  
Necessary And Sufficient

Given a pair T ≡ T 1 , T 2 of commuting subnormal Hilbert space operators, the Lifting Problem for Commuting Subnormals (LPCS) asks for necessary and sufficient conditions for the existence of a commuting pair N ≡ N 1 , N 2 of normal extensions of T 1 and T 2 ; in other words, T is a subnormal pair. The LPCS is a longstanding open problem in the operator theory. In this paper, we consider the LPCS of a class of powers of 2 -variable weighted shifts. Our main theorem states that if a “corner” of a 2-variable weighted shift T = W α , β ≔ T 1 , T 2 is subnormal, then T is subnormal if and only if a power T m , n ≔ T 1 m , T 2 n is subnormal for some m , n ≥ 1 . As a corollary, we have that if T is a 2-variable weighted shift having a tensor core or a diagonal core, then T is subnormal if and only if a power of T is subnormal.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj&gt; 0 for eachj&gt; 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

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