let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . in this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . as an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via the linear operator .

let s be a locally compact foundation semigroup with identity and                          be its semigroup algebra. let x be a weak*-closed left translation invariant subspace of    in this paper, we prove that  x  is invariantly  complemented in   if and  only if  the left ideal  of    has a bounded approximate identity. we also prove that a foundation semigroup with identity s is left amenab...

this paper is an investigation of $l$-dual frames with respect to a function-valued inner product, the so called $l$-bracket product on $l^{2}(g)$, where g is a locally compact abelian group with a uniform lattice $l$. we show that several well known theorems for dual frames and dual riesz bases in a hilbert space remain valid for $l$-dual frames and $l$-dual riesz bases in $l^{2}(g)$.

We estimate the rate of the pointwise approximation by operators of Bleimann, Butzer and Hahn of locally bounded functions, and of functions having a locally bounded derivative.

Let G be a locally compact Abelian group; I’ the dual group of G; CO(l_’)the algebra of continuous functions on r which vanish at infinity; CB(17)the continuous, bounded functions on r; M(G) the algebra of bounded Borel measures on G; Ll(G) the algebra of absolutely continuous measures; and M(G)A the algebra of l?ourier-Stielt jes transforms. Let E denote a compact subset of I’, and let A(E) be...

Image and audio data are examples of domains in which DPCM (Diierential Pulse Coded Modulation) is an eeective method for removing much of the linear correlation between data samples. However, most simple DPCM schemes cannot simultaneously cater for smooth signals, noisy signals, and discontinuities such as edges in images. To overcome this, many adaptive DPCM schemes have been proposed, includ...

in the region t>0. Here x =(Xl, x2 . . . . , xn), u =u(t, x), the f j , j = 1, 2, . . . , n, are continuously differentiable functions of a single real variable, and u0 (x) is in the class F; i.e., Uo(X) is a bounded function having locally bounded variation in the sense of TOt~LLI-CESARI. Moreover for each fixed t, u(t, x) is in the same class F. A function f is said to have bounded variation ...

We characterize semiperfect modules, semiperfect rings, and perfect rings using locally projective covers and generalized locally projective covers, where locally projective modules were introduced by Zimmermann-Huisgen and generalized locally projective coves are adapted from Azumaya’s generalized projective covers.