The sequence spaces ?p(?q2)(0?p<?) and ??(?q2) are introduced by using the q-difference operator ?q2 of second order. Apart from studying some basic properties these spaces, we construct basis obtain ?-, ?- ?-duals spaces. Besides matrix classes involving ?p(?q2) characterized. final section is devoted to classifying spectrum over space ?1 absolutely summable sequences.

We give two ”complementary” descriptions of the curve Γ parametrizing doubleBloch solutions to the difference analogue of the Lamé equation. The curve depends on a positive integer number l and two continuous parameters: the ”lattice spacing” η and the modular parameter τ . Apart from being a covering of the elliptic curve with the modular parameter τ , Γ is a hyperelliptic curve of genus 2l. W...

In present article the self-contained derivation of eigenvalue inverse problem results is given by using a discrete approximation with three-diagonal SturmLiouville operator on a finite interval. It is demonstrated that inverse problem procedure is nothing else than well known Gram-Schmidt orthonormalization in Euclidean space for special vectors numbered by space coordinate index. All the resu...

In this paper, we investigate the relationship between a meromorphic function f(z) and its difference operator when they share two sets, and give some interesting results.

In this paper we will study the existence of fundamental solutions for the explicit and implicit backward time dependent Schödinger equation, via discrete Fourier transform and its symbol for the Laplace operator. In both cases we will prove that the discrete fundamental solutions obtained converges to the continuous fundamental solution in the l1−norm sense.

In a recent paper by Hirzallah et al. [O. Hirzallah, F. Kittaneh, M. Krnić, N. Lovričević, and J. Pečarić. Eigenvalue inequalities for differences of means of Hilbert space operators. Linear Algebra and its Applications, 436:1516–1527, 2012.], several eigenvalue inequalities are obtained for the difference of weighted arithmetic and weighted geometric means of two positive invertible operators ...