مجله موجکها و جبر خطی
سال چهارم شماره 1 (Spring and Summer 2017)

Let K be a locally compact hypergroup with left Haar measure and let L1(K) be the complex Lebesgue space associated with it. Let L1(K) be the dual of L1(K). The purpose of this paper is to present some necessary and sucient conditions for L1(K) to have a topologically left invariant mean. Some characterizations of amenable hypergroups are given.

This paper is devoted to definition standard higher dimension shearlet group S = R Rn1 Rn and determination of squareintegrable subrepresentations of this group. Also we give a characterisation of admissible vectors associated with the Hilbert spaces corresponding to each subrepresentation.

In this paper, some algebraic and geometrical properties of the rank-k numerical hulls of normal matrices are investigated. A characterization of normal matrices whose rank-1 numerical hulls are equal to their numerical range is given. Moreover, using the extreme points of the numerical range, the higher rank numerical hulls of matrices of the form A1  iA2, where A1 and A2 are Hermitian, are investigated. The higher rank numerical hulls of the basic circulant matrix are also studied.

Frames in Hilbert bimodules are a special case of frames in HilbertC-modules. The paper considersA-frames and B-frames and their relationship in a Hilbert A-B-imprimitivity bimodule. Also, it is given that every frame in Hilbert spaces or Hilbert C-modules is a semi-tight frame. A relation betweenA-frames and K(HB)-frames is obtained in a Hilbert A-B-imprimitivity bimodule. Moreover, the last part of the paper investigates dual of an A-frame and a B-frame and presents a common property for all duals of a frame in a Hilbert A-B-imprimitivity bimodule.

The main results of this paper are generalizations of classical results from the numerical range to the block numerical range. A dierent and simpler proof for the Perron-Frobenius theory on the block numerical range of an irreducible nonnegative matrix is given. In addition, the Wielandt’s lemma and the Ky Fan’s theorem on the block numerical range are extended.

This paper describes and compares application of wavelet basis and Block-Pulse functions (BPFs) for solving fractional integrodi erential equation (FIDE) with a weakly singular kernel. First, a collocation method based on Haar wavelets (HW), Legendre wavelet (LW), Chebyshev wavelets (CHW), second kind Chebyshev wavelets (SKCHW), Cos and Sin wavelets (CASW) and BPFs are presented for driving approximate solution FIDEs with a weakly singular kernel. Error estimates of all proposed numerical methods are given to test the convergence and accuracy of the method. A comparative study of accuracy and computational time for the presented techniques is given.