Frame Decomposition of Decomposition Spaces

On the Decomposition of Hilbert Spaces

Basic relation between numerical range and Davis-Wielandt shell of an operator $A$ acting on a Hilbert space with orthonormal basis $xi={e_{i}|i in I}$ and its conjugate $bar{A}$ which is introduced in this paper are obtained. The results are used to study the relation between point spectrum, approximate spectrum and residual spectrum of $A$ and $bar{A}$. A necessary and sufficient condition fo...

On an atomic decomposition in Banach spaces

An atomic decomposition is considered in Banach space.  A method for constructing an atomic decomposition of Banach  space, starting with atomic decomposition of  subspaces  is presented. Some relations between them are established. The proposed method is used in the  study  of the  frame  properties of systems of eigenfunctions and associated functions of discontinuous differential operators.

Metrizability of Decomposition Spaces

Decomposition of Lebesgue Spaces

Decomposition of Besov-Morrey Spaces

We establish a decomposition of Besov-Morrey spaces in terms of smooth “wavelets” obtained from a Littlewood-Paley partition of unity, or more generally molecules concentrated on dyadic cubes. We show that an expansion in atoms supported on dyadic cubes holds. We study atoms in Morrey spaces and prove a Littlewood-Paley theorem. Our results extend those of M. Frazier and B. Jawerth for Besov sp...