What happens to the uncertainity relations along the process of gravitational collapses ? What is the position-space wave function of two finite volume massive bosons if we take contact interaction into account? What is the microscopic explanation in terms of particle exchanges of the force in the Casimir effect?

In this paper we derive optimal subspaces for Kolmogorov n-widths in the L2 norm with respect to sets of functions defined by kernels. This enables us to prove the existence of optimal spline subspaces of arbitrarily high degree for certain classes of functions in Sobolev spaces of importance in finite element methods. We construct these spline spaces explicitly in special cases. Math Subject C...

Let e ⊂ R be a finite union of disjoint closed intervals. We study measures whose essential support is e and whose discrete eigenvalues obey a 1/2-power condition. We show that a Szegő condition is equivalent to lim sup a1 · · · an cap(e) > 0 (this includes prior results of Widom and Peherstorfer–Yuditskii). Using Remling’s extension of the Denisov–Rakhmanov theorem and an analysis of Jost func...

This paper is concerned with a common element of the set of common fixed points for two infinite families of strictly pseudocontractive mappings and the set of solutions of a system of cocoercive quasivariational inclusions problems in Hilbert spaces. The strong convergence theorem for the above two sets is obtained by a novel general iterative scheme based on the viscosity approximation method...

Abstract. The semisimple Frobenius manifolds related to the Hurwitz spaces Hg,N(k1, . . . , kl) are considered. We show that the corresponding isomonodromic tau-function τI coincides with (−1/2)power of the Bergmann tau-function which was introduced in a recent work by the authors [8]. This enables us to calculate explicitly the G-function of Frobenius manifolds related to the Hurwitz spaces H0...

In this paper, we proposed a new two-step iteration scheme of hybrid mixed type for two asymptotically nonexpansive self mappings and two total asymptotically nonexpansive non-self mappings and establish some weak convergence theorems for mentioned scheme and mappings in the setting of uniformly convex Banach spaces. Our results extend and generalize several results from the current existing li...

* Correspondence: [email protected] College of Science, Civil Aviation University of China, Tianjin 300300, China Abstract Iterative algorithms have been extensively studied over the class of nonexpansive mappings in Hilbert spaces. Recall that nonexpansive mappings belong to quasinonexpansive mappings. The aim of this article is expanding the general approximation method proposed by Marino ...

This note is to indicate the new sphere of applicability of the method developed by Mlak as well as by the author. Restoring those ideas is summoned by current developments concerning K-spectral sets on numerical ranges. The decomposition of numerical ranges the title refers to is, see [13, p. 42], W(A⊕B) = conv(W(A) ∪ W(B)); (1) it can be proved for any two Hilbert space operators A and B. The...

A representation of the Jacobi algebra h1 ⋊ su(1, 1) by first order differential operators with polynomial coefficients on the manifold C×D1 is presented. The Hilbert space of holomorphic functions on which the holomorphic first order differential operators with polynomials coefficients act is constructed.

We provide the mathematical foundation for the Xm-Jacobi spectral theory. Namely, we present a self-adjoint operator associated to the differential expression with the exceptional Xm-Jacobi orthogonal polynomials as eigenfunctions. This proves that those polynomials are indeed eigenfunctions of the self-adjoint operator (rather than just formal eigenfunctions). Further, we prove the completenes...