Fractional powers of operators and Bessel potentials on Hilbert space

Michael Fisher

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Some generalizations of the hypersingular integral operators

Michael Fisher (1973)

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Bounds for Fractional Powers of Operators in a Hilbert Space and Constants in Moment Inequalities

I. Gil’, Michael (2009)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 47A56, 47A57,47A63 We derive bounds for the norms of the fractional powers of operators with compact Hermitian components, and operators having compact inverses in a separable Hilbert space. Moreover, for these operators, as well as for dissipative operators, the constants in the moment inequalities are established. * This research was supported by the Kamea Fund of Israel.

Fractional powers of non-densely defined operators

Celso Martinez, Miguel Sanz (1991)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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On some Schrödinger operators with a singular complex potential

Tosio Kato (1978)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Fractional powers of closed operators

H. Hövel, U. Westphal (1972)

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Fractional powers of non-negative operators in Fréchet spaces.

Martinez, C., Sanz, M., Calvo, V. (1989)

International Journal of Mathematics and Mathematical Sciences

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Fractional Powers of Almost Non-Negative Operators

Martínez, Celso, Sanz, Miguel, Redondo, Antonia (2005)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: Primary 47A60, 47D06. In this paper, we extend the theory of complex powers of operators to a class of operators in Banach spaces whose spectrum lies in C ]−∞, 0[ and whose resolvent satisfies an estimate ||(λ + A)(−1)|| ≤ (λ(−1) + λm) M for all λ > 0 and for some constants M > 0 and m ∈ R. This class of operators strictly contains the class of the non negative operators and the one of operators with polynomially bounded resolvent....

Generalized Fractional Calculus, Special Functions and Integral Transforms: What is the Relation? Обобщения на дробното смятане, специалните функции и интегралните трансформации: Каква е връзката?

Kiryakova, Virginia (2011)

Union of Bulgarian Mathematicians

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Виржиния С. Кирякова - В този обзор илюстрираме накратко наши приноси към обобщенията на дробното смятане (анализ) като теория на операторите за интегриране и диференциране от произволен (дробен) ред, на класическите специални функции и на интегралните трансформации от лапласов тип. Показано е, че тези три области на анализа са тясно свързани и взаимно индуцират своето възникване и по-нататъшно развитие. За конкретните твърдения, доказателства и примери, вж. Литературата. ...