It is shown that so called fundamental solutions the semiclassical expansions of which have been established earlier to be Borel summable to the solutions themselves appear also to be the unique solutions to the 1D Schrödinger equation having this property. Namely, it is shown in this paper that for the polynomial potentials the Borel function defined by the fundamental solutions can be conside...

We study the double scaling limit of $O(N)^3$-invariant tensor model, initially introduced in Carrozza and Tanasa, Lett. Math. Phys. (2016). This model has an interacting part containing two types quartic invariants, tetrahedric pillow one. For 2-point function, we rewrite sum over Feynman graphs at each order $1/N$ expansion as a \emph{finite} sum, where summand is function generating series m...

in this paper we introduce strongly $left[  v_{2},lambda_{2},m,pright]-$summable double vsequence spaces via orlicz function and examine someproperties of the resulting these spaces. also we give natural relationshipbetween these spaces and $s_{lambda_{2}}-$statistical convergence.

In this paper, we define and study q-statistical limit point, cluster q-statistically Cauchy, q-strongly Cesàro statistically C1q-summable sequences. We establish relationships of convergence with Further, apply to prove a Korovkin type approximation theorem.

Using the regenerative scheme of [8], we establish a functional central limit theorem (FCLT) for discrete time stochastic processes (chains) with summable memory decay. Furthermore, under stronger assumptions on the memory decay, we identify the limiting variance in terms of the process only. As applications, we define classes of binary autoregressive processes and power-law Ising chains for wh...

In this note we study the commutative modular and semisimple group rings of σ-summable abelian p-groups, which group class was introduced by R. Linton and Ch. Megibben. It is proved that S(RG) is σ-summable if and only if Gp is σ-summable, provided G is an abelian group and R is a commutative ring with 1 of prime characteristic p, having a trivial nilradical. If Gp is a σ-summable p-group and t...

We prove that the G\"{a}rtner--Ellis generating function of probability distributions associated with KMS states weakly interacting fermions on lattice can be written as limit logarithms Gaussian Berezin integrals. The covariances integrals are shown to have a uniform Pfaffian bound and summable in general cases interest, including systems not translation invariant. integral representation thus...

Let us observe that there exists a sequence of real numbers which is absolutely summable. Let us note that every sequence of real numbers which is summable is also convergent. Let us mention that every sequence of real numbers which is absolutely summable is also summable. Let us mention that there exists a sequence of real numbers which is absolutely summable. The following propositions are true: