Acta Mathematica Hungarica最新文献

We investigate optimal expansions of Kakeya sequences for the representation of real numbers. Expansions of Kakeya sequences generalize the expansions in non-integer bases and they display analogous redundancy phenomena. In this paper, we characterize optimal expansions of Kakeya sequences, and we provide conditions for the existence of unique expansions with respect to Kakeya sequences.

We establish the asymptotics of the second moment of the coefficient of (j)-th symmetric poower lift of classical Hecke eigenforms over certain polynomials, given by a sum of triangular numbers with certain positive coefficients. More precisely, for each (j in mathbb{N}), we obtain asymptotics for the sums given by

,where (lambda_{ sym^{j}f}^{2}(n)) denotes the coefficient of (j)-th symmetric power lift of classical Hecke eigenforms (f), the polynomials (alpha) and (beta) are given by

and

The aim in this note is to show that the variable Riesz potential operator (I_{alpha(cdot)}) embeds variable exponent grand Morrey spaces (L^{p(cdot)-0,nu(cdot),theta}(G)) into Campanato–Morrey spaces.

We investigate first Baire functionals on the dual ball of a separable Banach space (X) which are pointwise limit of a sequence of (X) whose closed span does not contain any copy of (ell_1) (or has separable dual). We propose an example of a (C(K)) space where not all such first Baire functionals exhibit this behavior. As an application, we study a quantitative version, in terms of descriptive set theory, of family a separable Banach spaces with this peculiarity.

We generalize two results about conjugacy class sizes of real elements to sub-class sizes of real elements.

Using a modification of the adapted Riccati transformation, weprove an oscillation criterion for generalizations of linear and half-linear Euler differenceequations. Our main result complements a large number of previouslyknown oscillation criteria about several similar generalizations of Euler differenceequations. The major part of this paper is formed by the proof of the main theorem.To illustrate the fact that the presented criterion is new even for linearequations with periodic coefficients, we finish this paper with the correspondingcorollary together with concrete examples of simple equations whose oscillatoryproperties do not follow from previously known criteria.

For an infinite family of real biquadratic fields k we give the structure of the Iwasawa module (X=X(k_{infty})) of the (mathbb{Z}_{2})-extension of k. For these fields, we obtain that (lambda=mu=0 mbox{ and }nu=2). where (lambda), (mu) and (nu) are the Iwasawa invariants of the cyclotomic (mathbb{Z}_{2})-extension of k

This paper aims to study some important topological properties of the regular topology on C(X, Y), the set of all continuous functions from a Tychonoff space X to a metric space (Y, d). In particular, we study in detail the connectedness of the regular topology on C(X, Y). In the end, some important countability properties are studied.

We deal with the class of Hausdorff spaces having a (pi)-base whose elements have an H-closed closure. Carlson proved that (|X|leq 2^{wL(X)psi_c(X)t(X)}) for every quasiregular space (X) with a (pi)-base whose elements have an H-closed closure. We provide an example of a space (X) having a (pi)-base whose elements have an H-closed closure which is not quasiregular (neither Urysohn) such that (|X|> 2^{wL(X)chi(X)}) (then (|X|> 2^{wL(X)psi_c(X)t(X)})). Always in the class of spaces with a (pi)-base whose elements have an H-closed closure, we establish the bound (|X|leq2^{wL(X)k(X)}) for Urysohn spaces and we give an example of an Urysohn space (Z) such that (k(Z)<chi(Z)). Lastly, we present some equivalent conditions to the Martin's Axiom involving spaces with a (pi)-base whose elements have an H-closed closure and, additionally, we prove that if a quasiregular space has a (pi)-base whose elements have an H-closed closure then such a space is Baire.