the series on the right of (3) being called the Fourier Eigenfunction Series and a. the Fourier Coefficients of f(x, y). I have studied elsewhere' the problem of convergence and summability of a Fourier Eigenfunction Series. In this note I am interested in announcing a result on uniqueness of eigenfunction expansion. Actually, we have thfe following, THEOREM. Let us suppose we are given an eige...

Uniform upper bounds and the asymptotic expansion with an explicit remainder term are established for Macdonald function Kiτ(x). The results can be applied, instance, to study summability of divergent Kontorovich-Lebedev integrals in sense Jones. Namely, we answer affirmatively a question (cf. [Ehrenmark U. Summability experiments class inverse transforms. Comput Math Appl. 2018;76(1):141–154.]...

A general theorem concerning many absolute summability methods is proved. 2000 Mathematics Subject Classification. 40F05, 40G05, 40D15, 40D25.

We have proved a theorem on |T, p n | k summability methods. This theorem includes a known theorem.

Let (un) be a sequence of real numbers and L be an additive summability method with some property. We show that if slow decrease of (un) or one-sided boundedness of the classical control modulo of the oscillatory behavior of (un) is a Tauberian condition for a general summability method L, then one-sided boundedness by a sequence with certain conditions of the general control modulo of the osci...

In this note we give some summability results for entropy solutions of the nonlinear parabolic equation ut − div ap(x,∇u) = f in ]0, T [×Ω with initial datum in L1(Ω) and assuming Dirichlet’s boundary condition, where ap(., .) is a Carathéodory function satisfying the classical Leray-Lions hypotheses, f ∈ L1(]0, T [×Ω) and Ω is a domain in RN . We find spaces of type Lr(0, T ;Mq(Ω)) containing ...

The classical summability methods of Borel (B) and Euler (E(λ), λ > 0) play an important role in many areas of mathematics. For instance, in summability theory they are perhaps the most important methods other than the Cesàro (Cα) and Abel (A) methods, and two chapters of the classic book of Hardy (1949) are devoted to them. In probability, the distinction between methods of Cesàro-Abel and Eul...