scholarly journals Fractional powers of operators

1988 ◽  
Vol 40 (2) ◽  
pp. 331-347 ◽  
Author(s):  
Celso MARTINEZ ◽  
Miguel SANZ ◽  
Luis MARCO
Keyword(s):  
Fractional Powers ◽  
Fractional Powers Of Operators

A distributional theory of fractional calculus

1985 ◽  
Vol 99 (3-4) ◽  
pp. 347-357 ◽  
Author(s):  
W. Lamb
Keyword(s):  
Fractional Calculus ◽  
Spectral Properties ◽  
Fractional Integration ◽  
Integral Operators ◽  
Fractional Integrals ◽  
Fractional Powers ◽  
Fractional Powers Of Operators ◽  
Fractional Integrals And Derivatives

SynopsisIn this paper, a theory of fractional calculus is developed for certain spacesD′p,μof generalised functions. The theory is based on the construction of fractionalpowers of certain simple differential and integral operators. With the parameter μ suitably restricted, these fractional powers are shown to coincide with the Riemann-Liouville and Weyl operators of fractional integration and differentiation. Standard properties associated with fractional integrals and derivatives follow immediately from results obtained previously by the author on fractional powers of operators; see [6], [7]. Some spectral properties are also obtained.

Fractional powers of operators and Riesz fractional integrals

1989 ◽  
Vol 112 (3-4) ◽  
pp. 237-247 ◽  
Author(s):  
S. E. Schiavone
Keyword(s):  
Banach Spaces ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integrals ◽  
Fréchet Spaces ◽  
Test Functions ◽  
Fractional Powers ◽  
Fractional Integral Operators ◽  
Fractional Powers Of Operators

SynopsisIn this paper, a theory of fractional powers of operators due to Balakrishnan, which is valid for certain operators on Banach spaces, is extended to Fréchet spaces. The resultingtheory is shown to be more general than that developed in an earlier approach by Lamb, and is applied to obtain mapping properties of certain Riesz fractional integral operators on spaces of test functions.

scholarly journals Fractional powers of operators defined on a Fréchet space

1984 ◽  
Vol 27 (2) ◽  
pp. 165-180 ◽  
Author(s):  
W. Lamb
Keyword(s):  
Banach Space ◽  
Fractional Power ◽  
Fréchet Space ◽  
Frechet Space ◽  
Fractional Powers ◽  
Fractional Powers Of Operators ◽  
Image Position ◽  
Densely Defined

The problem of finding a suitable representation for a fractional power of an operator defined in a Banach space X has, in recent years, attracted much attention. In particular, Balakrishnan [1], Hovel and Westphal [3] and Komatsu [4] have examined the problem of defining the fractionalpower (–A)α for closed densely-defined operators A such that

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