Integral transform is one of the techniques in function transformation methods. transforms have been interesting tools for solving different problems arising applied mathematics, mathematical physics and engineering science at least two centuries. We studied an extended fractional Mellin generalized sense. For this testing space E its dual E* are considered. investigated inversion formula by us...

In representations using frames, oblique duality appears in situations where the analysis and synthesis has to be done different subspaces. some cases, we cannot obtain an explicit expression for duals others there exists only one dual frame which not properties need. Also, practice computations are exact. To give a solution these problems, this work introduce investigate notion of approximate ...

Let $(X,d)$ be an infinite compact metric space, let $(B,parallel . parallel)$ be a unital Banach space, and take $alpha in (0,1).$ In this work, at first we define the big and little $alpha$-Lipschitz vector-valued (B-valued) operator algebras, and consider the little $alpha$-lipschitz $B$-valued operator algebra, $lip_{alpha}(X,B)$. Then we characterize its second dual space.

Controlled frames have been introduced to improve the numerical efficiency of iterative algorithms for inverting the frame operator on abstract Hilbert spaces. Fusion frames and g-frames generalize frames. Hilbert C*-modules form a wide category between Hilbert spaces and Banach spaces. Hilbert C*-modules are generalizations of Hilbert spaces by allowing the inner product to take values in a C*...

In the signal-processing literature, a frame is mechanism for performing analysis and reconstruction in Hilbert space. By contrast, quantum theory, positive operator-valued measure (POVM) decomposes Hilbert-space vector purpose of computing measurement probabilities. Frames their most common generalizations can be seen to give rise POVMs, but does every reasonable POVM arise from type frame? We...

In view of the good properties of nonstationary wavelet frames and the better flexibility of wavelets in Sobolev spaces, the nonstationary dual wavelet frames in a pair of dual Sobolev spaces are studied in this paper. We mainly give the oblique extension principle and the mixed extension principle for nonstationary dual wavelet frames in a pair of dual Sobolev spaces H(R) and H−s(Rd). Keywords...

in this note‎, ‎we aim to show that several known generalizations of frames are equivalent to the continuous frame‎ ‎defined by ali et al‎. ‎in 1993‎. ‎indeed‎, ‎it is shown that these generalizations can be considered as an operator between two hilbert spaces‎.