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On bases in Banach spaces

Tomek Bartoszyński, Mirna Džamonja, Lorenz Halbeisen, Eva Murtinová, Anatolij Plichko (2005)

Studia Mathematica

We investigate various kinds of bases in infinite-dimensional Banach spaces. In particular, we consider the complexity of Hamel bases in separable and non-separable Banach spaces and show that in a separable Banach space a Hamel basis cannot be analytic, whereas there are non-separable Hilbert spaces which have a discrete and closed Hamel basis. Further we investigate the existence of certain complete minimal systems in as well as in separable Banach spaces.

On Bell's duality theorem for harmonic functions

Joaquín Motos, Salvador Pérez-Esteva (1999)

Studia Mathematica

Define h ( E ) as the subspace of C ( B ̅ L , E ) consisting of all harmonic functions in B, where B is the ball in the n-dimensional Euclidean space and E is any Banach space. Consider also the space h - ( E * ) consisting of all harmonic E*-valued functions g such that ( 1 - | x | ) m f is bounded for some m>0. Then the dual h ( E * ) is represented by h - ( E * ) through f , g 0 = l i m r 1 ʃ B f ( r x ) , g ( x ) d x , f h - ( E * ) , g h ( E ) . This extends the results of S. Bell in the scalar case.

On Besov spaces and absolute convergence of the Fourier transform on Heisenberg groups

Leszek Skrzypczak (1998)

Commentationes Mathematicae Universitatis Carolinae

In this paper the absolute convergence of the group Fourier transform for the Heisenberg group is investigated. It is proved that the Fourier transform of functions belonging to certain Besov spaces is absolutely convergent. The function spaces are defined in terms of the heat semigroup of the full Laplacian of the Heisenberg group.

On bibasic systems and a Retherford’s problem

Anatoli Pličko, Paolo Terenzi (1984)

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

Ogni spazio di Banach ha un sistema bibasico ( x n , f n ) normalizzato; inoltre ogni successione ( x n ) uniformemente minimale appartiene ad un sistema biortogonale limitato ( x n , f n ) , dove ( f n ) è M-basica e normante.

Currently displaying 201 – 220 of 1948