The Fourier transform has been a major tool in analysis for over 100 years. However, it solely provides frequency information, and hides (in its phases) information concerning the moment of emission and duration of a signal. D. Gabor resolved this problem in 1946 [93] by introducing a fundamental new approach to signal decomposition. Gabor’s approach quickly became the paradigm for this area, b...

In my contribution I will provide an outline of how two major strands in Löbner’s work can be combined in a dynamic game-theoretical semantics: phase quantiVcation (PQ) and frame theory (FT). In a Vrst step a formal analysis of PQ in (dynamic) arrow logic is presented. Based on this analysis it is shown in the second step that frame theory must not be understood as being an alternative to stand...

This paper develops a boundedly rational version of variable frame theory (VFT) of Bacharach [B93] by merging the variable frame conceptual apparatus with the leveln theory (LNT) of Stahl and Wilson [SW95]. A fundamental feature of VFT is that a player’s options are determined by her ‘frame’: one ‘option’ is associated to each cell of a frame-induced partition of the actions. Coupled with the p...

In this talk, I give a very brief introduction to orthonormal bases for Hilbert spaces, and how they can be naturally generalized to similar families known as frames. In addition, I will show that frames possess many of the desirable properties that we require of and ONB, but without many of the restrictions. NOTE: This talk was first given by Dr. Rochus Boerner to the FRG Research group in Apr...

This is the first part of a series of notes [3, 4, 5, 6, 7] on frames, with several more to come. In this part I set down the basic definitions and properties, give a few examples, and begin the discussion of nuclei. The last section looks at various categorical properties, and could be omitted at a first reading. 1 After that you should read [4] and [5] in the order you prefer. That will give ...

Controlled frames in Hilbert spaces have been recently introduced by P. Balazs and etc. for improving the numerical efficiency of interactive algorithms for inverting the frame operator. In this paper we develop a theory based on g-fusion frames on Hilbert spaces, which provides exactly the frameworks not only to model new frames on Hilbert spaces but also for deriving robust operators. In part...

the theory of c-frames and c-bessel mappings are the generalizationsof the theory of frames and bessel sequences. in this paper, weobtain several equivalent conditions for dual of c-bessel mappings.we show that for a c-bessel mapping $f$, a retrievalformula with respect to a c-bessel mapping $g$ is satisfied if andonly if $g$ is sum of the canonical dual of $f$ with a c-besselmapping which  wea...

in this paper, we characterize multiresolution analysis(mra) parseval frame multiwavelets in l^2(r^d) with matrix dilations of the form (d f )(x) = sqrt{2}f (ax), where a is an arbitrary expanding dtimes d matrix with integer coefficients, such that |deta| =2. we study a class of generalized low pass matrix filters that allow us to define (and construct) the subclass of mra tight frame multiwav...