The Fourier-Transform, a basic discipline in electronic engineering, has two aspects, a mathematical one and a technical one. With the use of standard Fourier-Pairs and FourierTransform rules, thought patterns are supplied for the understanding of signals in the context of technical systems. As an educational aid a tutoring system has been developed covering the technical range of the topic Fou...

— We show that the Fourier-Laplace transform of a regular holonomic module over the Weyl algebra of one variable, which generically underlies a variation of polarized Hodge structure, underlies itself an integrable variation of polarized twistor structure. Résumé (Transformation de Fourier-Laplace d’une variation de structure de Hodge complexe polarisée) Nous montrons que le transformé de Fouri...

Given the nilpotent cone of a complex reductive Lie algebra, we consider its equivariant constructible derived category of sheaves with coefficients in an arbitrary field. This category and its subcategory of perverse sheaves play an important role in Springer theory and the theory of character sheaves. We show that the composition of the Fourier–Sato transform on the Lie algebra followed by re...

We introduce a concept of a quantum wide sense stationary process taking values in a C*-algebra and expected in a sub-algebra. The power spectrum of such a process is defined, in analogy to classical theory, as a positive measure on frequency space taking values in the expected algebra. The notion of linear quantum filters is introduced as some simple examples mentioned. 1 Spectral Analysis of ...

Wavelets, known to be useful in non-linear multi-scale processes and in multi-resolution analysis, are shown to have a q-deformed algebraic structure. The translation and dilation operators of the theory associate with any scaling equation a non-linear, two parameter algebra. This structure can be mapped onto the quantum group suq(2) in one limit, and approaches a Fourier series generating alge...

Introduction. We let G denote an infinite compact group, and G its dual. We use the notation of our book [3, Chapters 7 and 8]. Recall that -4(G) denotes the Fourier algebra of G (an algebra of continuous functions on G), and J2f°°(G) denotes its dual space under the pairing ( / , # ) , ( / G A (G), 0 Ç if°°(G)). Further, note if°°(G) is identified with the G*-algebra of bounded operators on L(...

Abstract In this work, we investigate the near horizon and asymptotic symmetries of static rotating hairy-AdS black hole in framework general minimal massive gravity. We obtain energy, angular momentum entropy solutions. Then show that our results for these quantities are consistent with first law thermodynamics. By considering geometry hole, find conserved charges their algebra. writing algebr...

We derive two new algorithms for reconstructing a discretetime 1-D signal from the phase of its discrete-time Fourier transform (DTFT) at irregular frequencies. Previous algorithms for this problem have either required the computation of a matrix nullspace, requiring O(N) computations, or have been iterative in nature; for the latter, the irregularity of the frequency samples precludes use of t...

In this paper, we investigate, for a locally compact groupG, the operator amenability of the Fourier-Stieltjes algebra B(G) and of the reduced Fourier-Stieltjes algebra Br(G). The natural conjecture is that any of these algebras is operator amenable if and only if G is compact. We partially prove this conjecture with mere operator amenability replaced by operator C-amenability for some constant...