Decomposition in a basis: (b j) j∈J basis of L 2 ([0, 1]). ∀f ∈ L 2 ([0, 1], f = j∈J f, b j b j with f, b j = 1 0 f (t)b j (t)dt. The Parseval-Bessel norm energy conservation equality yields f 2 = j∈J |f, b j | 2 1.2 Linear and non linear approximation For any I ∈ P(J), one defines f |I by f |I = j∈I f, b j b j. The question is now how to select " a good subset " of a given size M. A first poss...

In this paper, we are devoted to finding Goethals–Seidel sequences by using k-partition, and based on the finite Parseval relation, construction of could be transformed associated polynomials. Three different structures will presented. We first propose a method T-matrices directly obtain quad sequences. Next, introducing utilize two classes 8-partitions new class polynomials still remaining sam...

In this paper, we study the finite Gabor system for oversampling schemes. A characterization of dual tight frame using discrete time Zak transform is given. Also, a method to calculate coefficients expansion in case and necessary sufficient condition existence biorthogonal pair Riesz basis l2(ZL) Further, introduce notion block sliding Fourier (BSDFT) which reduces computational complexity give...

In this paper, we consider the non-homogeneous wave equation generated by Bessel operator. We prove existence and uniqueness of solution The representation is given. obtained a priori estimates in Sobolev type space. This problem was firstly considered work M. Assal [1] setting Bessel-Kingman hypergroups. technique used based on convolution theorem related estimates. Here, use different approac...