Positivity Conditions for Operators with Difference Kernels in Reflexive Spaces

Using methods of the theory of discrete and intFourier transforms, we obtain necessary and sufficient conditions for of the positivity of linear discrete, integral, and integro-differential operators with difference kernels in the spaces ℓ p and L p for 1 < p < ∞ and present examples illustrat...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 250; no. 5; pp. 717 - 727
Main Author Askhabov, S. N.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.11.2020
Springer
Springer Nature B.V
Subjects
Differential equations
Kernels
Mathematics
Mathematics and Statistics
Operators (mathematics)
singular operator
47G20
47G10
convolution operator
generalized operator of potential type
positive operator
integro-differential operator
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ISSN1072-3374
1573-8795
DOI10.1007/s10958-020-05036-0

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Summary:Using methods of the theory of discrete and intFourier transforms, we obtain necessary and sufficient conditions for of the positivity of linear discrete, integral, and integro-differential operators with difference kernels in the spaces ℓ p and L p for 1 < p < ∞ and present examples illustrating the results obtained.
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ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-020-05036-0