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Function spaces of Nikolskii type on compact manifold

Cristiana Bondioli (1992)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Nikolskii spaces were defined by way of translations on R n and by way of coordinate maps on a differentiable manifold. In this paper we prove that, for functions with compact support in R n , we get an equivalent definition if we replace translations by all isometries of R n . This result seems to justify a definition of Nikolskii type function spaces on riemannian manifolds by means of a transitive group of isometries (provided that one exists). By approximation theorems, we prove that - for homogeneous...

Function spaces on the snowflake

Maryia Kabanava (2011)

Banach Center Publications

We consider two types of Besov spaces on the closed snowflake, defined by traces and with the help of the homeomorphic map from the interval [0,3]. We compare these spaces and characterize them in terms of Daubechies wavelets.

Function theory in sectors

Brian Jefferies (2004)

Studia Mathematica

It is shown that there is a one-to-one correspondence between uniformly bounded holomorphic functions of n complex variables in sectors of ℂⁿ, and uniformly bounded functions of n+1 real variables in sectors of ℝ n + 1 that are monogenic functions in the sense of Clifford analysis. The result is applied to the construction of functional calculi for n commuting operators, including the example of differentiation operators on a Lipschitz surface in ℝ n + 1 .

Functional calculus for a class of unbounded linear operators on some non-archimedean Banach spaces

Dodzi Attimu, Toka Diagana (2009)

Commentationes Mathematicae Universitatis Carolinae

This paper is mainly concerned with extensions of the so-called Vishik functional calculus for analytic bounded linear operators to a class of unbounded linear operators on c 0 . For that, our first task consists of introducing a new class of linear operators denoted W ( c 0 ( J , ω , 𝕂 ) ) and next we make extensive use of such a new class along with the concept of convergence in the sense of resolvents to construct a functional calculus for a large class of unbounded linear operators.

Functional calculus in weighted group algebras.

Jacek Dziubanski, Jean Ludwig, Carine Molitor-Braun (2004)

Revista Matemática Complutense

Let G be a compactly generated, locally compact group with polynomial growth and let ω be a weight on G. We look for general conditions on the weight which allow us to develop a functional calculus on a total part of L1(G,ω). This functional calculus is then used to study harmonic analysis properties of L1(G,ω), such as the Wiener property and Domar's theorem.

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