Atomic characterizations of modulation spaces through Gabor-type representations

Atomic characterizations of vector-valued function spaces

The rst part of this diploma thesis deals with the topic of nding equivalent norms and characterizations for vector-valued Besov and Triebel-Lizorkin spaces Bs p,q(E) and F s p,q(E). We will deduce general criteria by transferring and extending a theorem of Bui, Paluszy«ski and Taibleson from the scalar to the vector-valued case. By using special norms and characterizations we will derive neces...

The Representations and Positive Type Functions of Some Homogenous Spaces

‎For a homogeneous spaces ‎$‎G/H‎$‎, we show that the convolution on $L^1(G/H)$ is the same as convolution on $L^1(K)$, where $G$ is semidirect product of a closed subgroup $H$ and a normal subgroup $K $ of ‎$‎G‎$‎. ‎Also we prove that there exists a one to one correspondence between nondegenerat $ast$-representations of $L^1(G/H)$ and representations of ...

Intrinsic atomic characterizations of function spaces on domains

Flexible Gabor - wavelet atomic decompositions for L 2 - Sobolev spaces

In this paper we present a general construction of frames, which allows one to ensure that certain families of functions (atoms) obtained by a suitable combination of translation, modulation, and dilation will form Banach frames for the family of L2-Sobolev spaces on R of any order. In this construction a parameter α ∈ [0, 1) governs the dependence of the dilation factor on the frequency parame...

Spline-type Spaces in Gabor Analysis