The main aim of this article is to generalize the notion of almost convergent, Cesàro summable and lacunary summable spaces by using a generalized difference operator defined associating a sequence of non-zero scalars and characterize some matrix classes involving these sequence spaces. In this article we also introduce the idea of difference infinite matrices. It is expected that these investi...

We prove that if a multiple trigonometric series is spherically Abel summable everywhere to an everywhere finite function f(x) which is bounded below by an integrable function, then the series is the Fourier series of f(x) if the coefficients of the multiple trigonometric series satisfy a mild growth condition. As a consequence, we show that if a multiple trigonometric series is spherically con...

In this paper we analyze the Banach *-algebra of time-frequency shifts with absolutely summable coefficients. We prove a noncommutative version of the Wiener lemma. We also construct a faithful tracial state on this algebra which implies the algebra contains no compact operators. As a corollary we obtain a special case of the Heil-Ramanathan-Topiwala conjecture regarding linear independence of ...

The paper contains a new prof for the sufficiency in Joel H. Shapiro’s recent characterization of inner functions saying that an analytic selfmap φ of the open unit disk is an inner function if and only if the essential norm of the composition operator of symbol φ is equal to √ 1+|φ(0)| 1−|φ(0)| . The main ingredient in the proof is a formula for the essential norm of a composition operator in ...

A weakly stationary process with summable partial autocorrelations is proved to have one-sided autoregressive and moving average representations. Sums of autocorrelations and alternating autocorrelations are expressed as products of simple rational functions of partial autocorrela-tions. A general bound for sums of squared autocorrelations in terms of partial autocorrelations is also obtained.