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A note on a formula for the fractional powers of infinitesimal generators of semigroups

100%

Martinez C., Sanz M.

Studia Mathematica

1996

tom 119

nr 3

247-254

If -A is the generator of an equibounded $C_0$-semigroup and 0 < Re α < m (m integer), its fractional power $A^α$ can be described in terms of the semigroup, through a formula that is only valid if a certain function $K_{α,m}$ is nonzero. This paper is devoted to the study of the zeros of $K_{α,m}$.

Suitable domains to define fractional integrals of Weyl via fractional powers of operators

81%

Martínez C., Redondo A., Sanz M.

Studia Mathematica

2011

tom 202

nr 2

145-164

We present a new method to study the classical fractional integrals of Weyl. This new approach basically consists in considering these operators in the largest space where they make sense. In particular, we construct a theory of fractional integrals of Weyl by studying these operators in an appropriate Fréchet space. This is a function space which contains the $L^{p}(ℝ)$-spaces, and it appears in a natural way if we wish to identify these fractional operators with fractional powers of a suitable non-negative operator. This identification allows us to give a unified view of the theory and provides some elegant proofs of some well-known results on the fractional integrals of Weyl.

Ograniczanie wyników

2 Studia Mathematica

2 Sanz M.

1 Martinez C.

1 Martínez C.

1 Redondo A.

1 2011

1 1996

Wyniki wyszukiwania

A note on a formula for the fractional powers of infinitesimal generators of semigroups

Suitable domains to define fractional integrals of Weyl via fractional powers of operators