Rotundity and smoothness in conjugate spaces

Control and Cybernetics Rotundity, Smoothness and Duality

The duality between smoothness and rotundity of functions is studied in a nonlinear abstract framework. Here smoothness is enlarged to subdifferentiability properties and rotundity is formulated by means of approximation properties.

A Bornological Approach to Rotundity and Smoothness Applied to Approximation

In this paper we are interested in examining the geometry of a bounded convex function over a Banach space via its subdiierential mapping. We will consider two concepts. The rst is the single valuedness and continuity of the subdiierential mapping, and the second is the single valuedness and the continuity of the \inverse" of this mapping. The smoothness of f is important for the rst concept as...

On X ̃-frames and conjugate systems in Banach spaces

The generalization of p-frame in Banach spaces is considered in this paper. The concepts of an $tilde{X}$-frame and a system conjugate to $tilde{X}$-frame were introduced. Analogues of the results on the existence of conjugate system were obtained. The stability of $tilde{X}$-frame having a conjugate system is studied.

Extreme Points and Rotundity of Orlicz-sobolev Spaces

Shearlet Smoothness Spaces

The shearlet representation has gained increasingly more prominence in recent years as a flexible mathematical framework which enables the efficient analysis of anisotropic phenomena by combining multiscale analysis with the ability to handle directional information. In this paper, we introduce a class of shearlet smoothness spaces which is derived from the theory of decomposition spaces recent...