We discuss the large order behaviour and Borel summability of the topological expansion of models of 2D gravity coupled to general (p, q) conformal matter. In a previous work it was proven that at large order k the string susceptibility had a generic a k Γ(2k − 1 2) behaviour. Moreover the constant a, relevant for the problem of Borel summability, was determined for all one-matrix models. We he...

In this paper, determining the operator norm, we give certain characterizations of matrix transformations from space $ \left\vert \overline N_p^{\phi }\right\vert _{k}$, all series summable by absolute weighted mean summability method, to one classical sequence spaces $c_{0},c,l_{\infty }.$ Also, obtain necessary and sufficient conditions for each in these classes be compact establish a number ...

In this paper, a known theorem dealing with | C, 1 |k summability methods has been generalized under weaker conditions for | C, α, β ; δ |k summability methods. Some new results have also been obtained. AMS subject classifications: 40D15, 40F05, 40G99

*Correspondence: [email protected] 1Faculty of Education, Harran University, Şanlıurfa, Turkey Full list of author information is available at the end of the article Abstract New concepts of fλ,μ-statistical convergence for double sequences of order α̃ and strong fλ,μ-Cesàro summability for double sequences of order α̃ are introduced for sequences of (complex or real) numbers. Furthermore, we giv...

We consider perturbed Schrödinger equation, which is an elliptic operator with unbounded coefficients. We use wavelets adapted to Schrödinger operator to deal with problems on unbounded domain. The wavelets are constructed from Hermite functions, which characterizes the space generated by the Schrödinger operator. We show that the Galerkin matrix can be preconditioned by a diagonal matrix so th...

Let X and Y be two sequence spaces and A = (ank) be an infinite matrix. If for each x ∈ X the series An(x) = ∑∞ k=0 ankxk converges for each n and the sequence Ax = (Anx) ∈ Y we say that the matrix A maps X into Y . By (X,Y ) we denote the set of all matrices which map X into Y . Let c be the set of all convergent sequences. A matrix A is called regular if A ∈ (c, c) and limn→∞Anx = limk→∞ xk f...

In this paper we obtain appropriate necessary and sufficient conditions for |N, pn|k summability to imply that of |N,qn|s for 1< k≤ s<∞. As in [6] we make use of a result of Bennett [1], who has obtained necessary and sufficient conditions for a factorable matrix to map lk → ls. A factorable matrix A is one in which each entry ank = bnck. Weighted mean matrices are factorable. It will not be po...

Abstract This paper explores the possibility for summing Fourier series nonlinearly via Pythagorean harmonic mean. It reports on new results this summability with introduction of concepts like smoothing operator and semi-harmonic summation. The is demonstrated to be Kalman filtering linear summability, logistic processing linearized summability. An emerging direct inapplicability seismic-like s...

Let A = (ank)∞n,k=1 be an infinite matrix and x = (xk) ∞ k=1 a sequence of real or complex numbers. Then the A-transform of x is a sequence Ax = (An(x))where An(x) = ∑ ∞ k=1 ankxk provided that the series converges for each n; and the sequence x is said to be A-summable if Ax is convergent. In this paper we define statistical A-summability of x, that is, x is said to be statistically A-summable...

and evaluating the generalized sum of (1) as the lim rm(x; f). The matrix ?2 will be subjected to the restrictions (i-iv) below. These restrictions are of such general nature, however, that they are satisfied by a great majority of the definitions of summability known in the literature. Our first condition on 21 is significant only in the case where 91 is of infinite reference. It is automatica...