Related papers: Bounded convergence theorem for abstract Kurzweil-…
In this article, we provide a unified framework for studying the convergence of rescaled characteristic polynomials of random matrices from various classical ensembles as well as functional convergence results for the Riemann zeta function.…
A version of the Lebesgue differentiation theorem is offered, where the $L^p$ norm is replaced with any rearrangement-invariant norm. Necessary and sufficient conditions for a norm of this kind to support the Lebesgue differentiation…
We establish new Strichartz estimates for orthonormal systems on compact Riemannian manifolds in the case of wave, Klein-Gordon and fractional Schr\"odinger equations. Our results generalize the classical (single-function) Strichartz…
To every minimal model of a complete local isolated cDV singularity Donovan--Wemyss associate a finite dimensional symmetric algebra known as the contraction algebra. We construct the first known standard derived equivalences between these…
Recently, we have established and used the generalized Littlewood theorem concerning contour integrals of the logarithm of analytical function to obtain new criteria equivalent to the Riemann hypothesis. Later, the same theorem was applied…
Let K be a number field and let S be a finite set of places of K which contains all the Archimedean places. For any f(z) in K(z) of degree d at least 2 which is not a d-th power in \bar{K}(z), Siegel's theorem implies that the image set…
The classical Berry-Esseen error bound, for the normal approximation to the law of a sum of independent and identically distributed random variables, is here improved by replacing the standardised third absolute moment by a weak norm…
We introduce and investigate the Henstock-Kurzweil (HK) integral for Riesz-space-valued functions on time scales. Some basic properties of the HK delta integral for Riesz-space-valued functions are proved. Further, we prove uniform and…
Finite-part integration is a recently introduced method of evaluating convergent integrals by means of the finite part of divergent integrals [E.A. Galapon, {\it Proc. R. Soc. A 473, 20160567} (2017)]. Current application of the method…
In this paper a lower bound for solutions to the secular equation of the Schr\"odinger equation with basis functions discontinuous on boundaries of divided regions is given. If the functions do not have the discontinuity, the bound reduces…
We find the origin of the integration theory for multifunctions in the sixties in the pioneering works of G. Debreu and R. Aumann, Nobel prizes for the Economy in 1983 and in 2005, respectively. The Aumann integral is defined by means the…
Discrete analogs of the classical Kontorovich-Lebedev transforms are introduced and investigated. It involves series with the modified Bessel function or Macdonald function $K_{in}(x), x >0, n \in \mathbb{N}, i $ is the imaginary unit, and…
We consider the hard-edge scaling of the Mittag-Leffler ensemble confined to a fixed disk inside the droplet. Our primary emphasis is on fluctuations of rotationally-invariant additive statistics that depend on the radius and thus give rise…
Integration, just as much as differentiation, is a fundamental calculus tool that is widely used in many scientific domains. Formalizing the mathematical concept of integration and the associated results in a formal proof assistant helps in…
We give a new proof of the Kat\v{e}tov-Tong theorem. Our strategy is to first prove the theorem for compact Hausdorff spaces, and then extend it to all normal spaces. The key ingredient is how the ring of bounded continuous real-valued…
A key tool in recent advances in understanding arithmetic progressions and other patterns in subsets of the integers is certain norms or seminorms. One example is the norms on $\Z/N\Z$ introduced by Gowers in his proof of Szemer\'edi's…
In this paper, we establish some Strichartz estimates for orthonormal functions and probabilistic convergence of density functions related to compact operators on manifolds. Firstly, we present the suitable bound of $\int_{a\leq|s|\leq…
Assuming the Riemann Hypothesis, we derive explicit bounds for the error terms in short interval analogues of the prime number theorem and Mertens' theorems using a smoothing argument. Our results improve upon previous bounds in both…
This paper systematically studies the subset of continuous linear functionals on the projective tensor product of Banach spaces whose norms are bounded by Grothendieck's constant $K_G$. We term such functionals Grothendieck functional…
In this note we show that for analytic semigroups the so-called Weiss condition of uniform boundedness of the operators $Re(\lambda)^\einhalb C(\lambda+A)^{-1}, \qquad Re(\lambda)>0$ on the complex right half plane and weak Lebesgue…