Related papers: On multidimensional F. Riesz's "Rising Sun" Lemma
A lemma of Micchelli's, concerning radial polynomials and weighted sums of point evaluations, is shown to hold for arbitrary linear functionals, as is Schaback's more recent extension of this lemma and Schaback's result concerning…
The purpose of this paper is threefold. First the natural extension of Riesz potentials to the context of quasi metric measure spaces for the class of upper doubling measures are studied on Lebesgue spaces, obtaining necessary and…
In this paper we argue that modified Friedmann equations with a bounce solution can be derived from a modified dispersion relation by employing a thermodynamical description of general relativity on the apparent horizon.
We give an alternative proof of Suslin's equi-dimensionalization moving lemma using a different geometric construction. The new construction provides better control of the degrees of the polynomials describing the geometric procedure. The…
We prove some 3-adic congruences for binomial sums, which were conjectured by Sun.
Motivated by works on extension sets in standard domains we introduce a notion of the Carath\'eodory set that seems better suited for the methods used in proofs of results on characterization of extension sets. A special stress is put on a…
We consider a system of reaction-diffusion equations including chemotaxis terms and coming out of the modeling of multiple sclerosis. The global existence of strong solutions to this system in any dimension is proved, and it is also shown…
This note generalizes the notion of conditional probability to Riesz spaces using the order-theoretic approach. With the aid of this concept, we establish the law of total probability and Bayes' theorem in Riesz spaces; we also prove an…
In this paper we consider generalized Leontief model. We show that under certain condition the generalized Leontief model is solvable by iterative descent method based on infeasible interior point algorithm. We prove the convergence of the…
The notion of framings, recently emerging in P. G. Casazza, D. Han, and D. R. Larson, Frames for Banach spaces, in {\em The functional and harmonic analysis of wavelets and frames} (San Antonio, TX, 1999), {\em Contemp. Math}. {\bf 247}…
We prove that if a Bessel sequence in a Hilbert space, that is indexed by a countably infinite group in an invariant manner, can be partitioned into finitely many Riesz basic sequences, then each of the sets in the partition can be chosen…
We prove a fixed point theorem for a particular multifunction from the unit sphere of a reflexive Banach space with the Kadec-Klee property into itself.
We prove several extensions of the Erdos-Fuchs theorem.
Some difficulties regarding the application of the well-known sieve method are considered in the case when a practical (program) realization of selecting elements, having a particular property among the elements of a set with a sufficiently…
In this article we present Pickands theorem and his double sum method. We follow Piterbarg's proof of this theorem. Since his proof relies on general lemmas we present a complete proof of Pickands theorem using Borell inequality and Slepian…
Furstenberg-Weiss have extended Szemer\'edi's theorem on arithmetic progressions to trees by showing that a large subset of the tree contains arbitrarily long arithmetic subtrees. We study higher dimensional versions that analogously extend…
We generalize certain arguments in Zariski's irregularity theorem on cyclic multiple planes.
A quaternionic partial differential equation is shown to be a generalisation of the Riccati ordinary differential equation and its relationship with the Schrodinger equation is established. Various approaches to the problem of finding…
The Riemann hypothesis is proved by quantum-extending the zeta Riemann function to a quantum mapping between quantum $1$-spheres with quantum algebra $A=\mathbb{C}$, in the sense of A. Pr\'astaro \cite{PRAS01, PRAS02}. Algebraic topologic…
We give a simple proof of the increasing strengthening of Arhangel'skii's Theorem. Our proof naturally leads to a refinement of this result of Juh\'asz.