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Admissible functions for the Dirichlet space

Javad Mashreghi, Mahmood Shabankhah (2010)

Studia Mathematica

Zero sets and uniqueness sets of the classical Dirichlet space are not completely characterized yet. We define the concept of admissible functions for the Dirichlet space and then apply them to obtain a new class of zero sets for . Then we discuss the relation between the zero sets of and those of .

Algebras of differentiable functions on Riemann surfaces

Karel De Leeuw, H. Mirkil (1964)

Annales de l'institut Fourier

La structure d’une variété V indéfiniment différentiable est complètement caractérisée par l’algèbre des fonctions indéfiniment différentiables sur V . Pour des surfaces de Riemann il n’y a pas, en général, une algèbre caractérisante canonique de fonctions globalement définies. Dans ce travail l’on définit une classe dénombrable de telles algèbres. Ces algèbres sont des analogues, pour les surfaces de Riemann, des algèbres définies pour le plan par les auteurs dans “Algebras of differentiable functions...

Algebras of holomorphic functions with Hadamard multiplication

Hermann Render, Andreas Sauer (1996)

Studia Mathematica

A systematic investigation of algebras of holomorphic functions endowed with the Hadamard product is given. For example we show that the set of all non-invertible elements is dense and that each multiplicative functional is continuous, answering some questions in the literature.

Algebras of Toeplitz operators with oscillating symbols.

Albrecht Böttcher, Sergei M. Grudsky, Enrique Ramírez de Arellano (2004)

Revista Matemática Iberoamericana

This paper is devoted to Banach algebras generated by Toeplitz operators with strongly oscillating symbols, that is, with symbols of the form b[eia(x)] where b belongs to some algebra of functions on the unit circle and a is a fixed orientation-preserving homeomorphism of the real line onto itself. We prove the existence of certain interesting homomorphisms and establish conditions for the normal solvability, Fredholmness, and invertibility of operators in these algebras.

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