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On the bundle convergence of double orthogonal series in noncommutative L 2 -spaces

Ferenc Móricz, Barthélemy Le Gac (2000)

Studia Mathematica

The notion of bundle convergence in von Neumann algebras and their L 2 -spaces for single (ordinary) sequences was introduced by Hensz, Jajte, and Paszkiewicz in 1996. Bundle convergence is stronger than almost sure convergence in von Neumann algebras. Our main result is the extension of the two-parameter Rademacher-Men’shov theorem from the classical commutative case to the noncommutative case. To our best knowledge, this is the first attempt to adopt the notion of bundle convergence to multiple series....

On the existence of non-linear frames

Shah Jahan, Varinder Kumar, S.K. Kaushik (2017)

Archivum Mathematicum

A stronger version of the notion of frame in Banach space called Strong Retro Banach frame (SRBF) is defined and studied. It has been proved that if 𝒳 is a Banach space such that 𝒳 * has a SRBF, then 𝒳 has a Bi-Banach frame with some geometric property. Also, it has been proved that if a Banach space 𝒳 has an approximative Schauder frame, then 𝒳 * has a SRBF. Finally, the existence of a non-linear SRBF in the conjugate of a separable Banach space has been proved.

On the existence of wavelets for non-expansive dilation matrices.

Darrin Speegle (2003)

Collectanea Mathematica

Sets which simultaneously tile Rn by applying powers of an invertible matrix and translations by a lattice are studied. Diagonal matrices A for which there exist sets that tile by powers of A and by integer translations are characterized. A sufficient condition and a necessary condition on the dilations and translations for the existence of such sets are also given. These conditions depend in an essential way on the interplay between the eigenvectors of the dilation matrix and the translation lattice...

On the Hermite expansions of functions from the Hardy class

Rahul Garg, Sundaram Thangavelu (2010)

Studia Mathematica

Considering functions f on ℝⁿ for which both f and f̂ are bounded by the Gaussian e - 1 / 2 a | x | ² , 0 < a < 1, we show that their Fourier-Hermite coefficients have exponential decay. Optimal decay is obtained for O(n)-finite functions, thus extending a one-dimensional result of Vemuri.

On the representation systems with respect to summation methods

K. S. Kazarian (2006)

Banach Center Publications

Properties of representation systems with respect to summation methods are studied. For a given representation system with respect to a given summation method we study, in particular, the question of the stability of that property after deleting finitely many elements. As a consequence we obtain the existence of null series for the systems with respect to a given method of summation.

Open problems in constructive function theory.

Baratchart, L., Martínez-Finkelshtein, A., Jimenez, D., Lubinsky, D.S., Mhaskar, H.N., Pritsker, I., Putinar, M., Stylianopoulos, N., Totik, V., Varju, P., Xu, Y. (2006)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

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