In the present article, using generalized Bessel-Maitland transform, Laplace transform and other known transforms, authors obtain new Parseval-Goldstein type relations. Using these relations, some integrals involving Fox-Wright functions are evaluated. Illustrative examples also given.

We study the determinant line bundle over moduli space of stable bundles on abelian surfaces. We evaluate their analytic torsions. We extend Mukai's version of the Parseval Theorem to L 2 metrics on cohomology groups. We prove that the Mukai transform preserves the determinant line bundle as a hermitian line bundle. This is done by induction via the natural boundary of the moduli spaces.

We generalize the Second Oversampling Theorem for wavelet frames and dual wavelet frames from the setting of integer dilations to real dilations. We also study the relationship between dilation matrix oversampling of semi-orthogonal Parseval wavelet frames and the additional shift invariance gain of the core subspace.

A generalized filter construction is used to build non-MRA Parseval wavelets for dilation by 2 in L2(R2). These examples have the same multiplicity functions as wavelet sets, yet can be made to be Cr with Cr Fourier transform for any fixed positive integer r.

In [13] frames of subspaces extended to continuous version namely c-frame of subspaces. In this article we consider to the relations between cframes of subspaces and local c-frames. Also in this article we give some important relation about duality and parseval c-frames of subspaces.