DFG–Schwerpunktprogramm 1114 Mathematical methods for time series analysis and digital image processing Generalized Coorbit Theory, Banach Frames, and the Relation to α-Modulation Spaces
نویسندگان
چکیده
This paper is concerned with generalizations and specific applications of the coorbit space theory based on group representations modulo quotients that has been developed quite recently. We show that the general theory applied to the affine Weyl–Heisenberg group gives rise to families of smoothness spaces that can be identified with α-modulation spaces.
منابع مشابه
DFG–Schwerpunktprogramm 1114 Mathematical methods for time series analysis and digital image processing The Canonical Coherent States Associated With Quotients of the Affine Weyl-Heisenberg Group
This paper is concerned with the uncertainty principle in the context of the affine-Weyl-Heisenberg group in one and two dimensions. As the representation of this group fails to be square integrable, we explore various admissible sections of this group, and calculate the resulting uncertainty principles as well as its minimizers with respect to these sections. Previous studies have shown that t...
متن کاملGeneralized Coorbit Theory, Banach Frames, and the Relation to α–Modulation Spaces
This paper is concerned with generalizations and specific applications of the coorbit space theory based on group representations modulo quotients that has been developed quite recently. We show that the general theory applied to the affine Weyl–Heisenberg group gives rise to families of smoothness spaces that can be identified with α-modulation spaces.
متن کاملDFG–Schwerpunktprogramm 1114 Mathematical methods for time series analysis and digital image processing On the mathematical structure of direction and motion estimation
The natural characteristics of the considered signals and the statistics of the measurement noise are decisive for designing any kind of optimal estimation methods in signal processing. Astonishingly, this principle has so far only partially found its way into the field of motion estimation for image (or video) data, be it in the case of video communication or in physical precision metrology. W...
متن کاملDFG–Schwerpunktprogramm 1114 Mathematical methods for time series analysis and digital image processing Optimal Approximation of Elliptic Problems by Linear and Nonlinear Mappings III: Frames
We study the optimal approximation of the solution of an operator equation A(u) = f by certain n-term approximations with respect to specific classes of frames. We consider worst case errors, where f is an element of the unit ball of a Sobolev or Besov space Bt q(Lp(Ω)) and Ω ⊂ Rd is a bounded Lipschitz domain; the error is always measured in the Hs-norm. We study the order of convergence of th...
متن کاملFrames and Coorbit Theory on Homogeneous Spaces with a Special Guidance on the Sphere
The topic of this article is a generalization of the theory of coorbit spaces and related frame constructions to Banach spaces of functions or distributions over domains and manifolds. As a special case one obtains modulation spaces and Gabor frames on spheres. Group theoretical considerations allow first to introduce generalized wavelet transforms. These are then used to define coorbit spaces ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005