The aim of this paper is to show that, in various situations, the only continuous linear map that transforms a convolution product into a pointwise product is a Fourier transform. We focus on the cyclic groups Z/nZ, the integers Z, the Torus T and the real line. We also ask a related question for the twisted convolution. In memory of A. Hulanicki.

Let A = (a j ) be an orthogonal matrix with no entries zero. Let B = (b j ) be the matrix defined by b j = 1 ai j . M. Kontsevich conjectured that the rank of B is never equal to three. We interpret this conjecture geometrically and prove it. The geometric statment can be understood as a generalization of the Castelnouvo lemma and Brianchon’s theorem in algebraic geometry. §1. Definitions and S...

Suganya.M ,Nirmala.R 2 PG Scholar ,Dept of ECE, Vivekananda college of engineering for women Assistant professor ,Dept of ECE, Vivekananda college of engineering for women AbstractPower consumption and area reduction are one of the major issues in VLSI applications. The efficient realization of computational complexity for 2D DWT using convolution based generic structure. The proposed design sc...

in this paper, we deal with the subdierential concept onhadamard spaces. flat hadamard spaces are characterized, and nec-essary and sucient conditions are presented to prove that the subdif-ferential set in hadamard spaces is nonempty. proximal subdierentialin hadamard spaces is addressed and some basic properties are high-lighted. finally, a density theorem for subdierential set is establi...

Let A and B be n n positive semidefinite Hermitian matrices, let c and/ be real numbers, let o denote the Hadamard product of matrices, and let Ak denote any k )< k principal submatrix of A. The following trace and eigenvalue inequalities are shown: tr(AoB) <_tr(AoBa), c_<0or_> 1, tr(AoB)a_>tr(AaoBa), 0_a_ 1, A1/a(A o Ba) <_ Al/(Az o B), a <_ /,a O, Al/a[(Aa)k] <_ A1/[(A)k], a <_/,a/ 0. The equ...

Fej'{e}r  Hadamard  inequality is generalization of Hadamard inequality. In this paper we prove certain Fej'{e}r  Hadamard  inequalities for $k$-fractional integrals. We deduce Fej'{e}r  Hadamard-type  inequalities for Riemann-Liouville fractional integrals. Also as special case Hadamard inequalities for $k$-fractional as well as fractional integrals are given.