Related papers: The Lieb-Thirring inequalities: Recent results and…
This book is not meant to be another compendium of select inequalities, nor does it claim to contain the latest or the slickest ways of proving them. This project is rather an attempt at describing how most functional inequalities are not…
We present some old and new results on dispersive estimates for Schroedinger equations.
Some mathematical inequalities among various weighted means are studied. Inequalities on weighted logarithmic mean are given. Besides, the gap in Jensen's inequality is studied as a convex function approach. Consequently, some non-trivial…
I review and discuss a selected sample of recent results in pNRQCD.
I examine the results obtained so far in exploring the recent proposal of theories of the relativistic transformations between inertial observers that involve both an observer-independent velocity scale and an observer-independent…
We survey recent work on local well-posedness results for parabolic equations and systems with rough initial data.
We consider the Brascamp--Lieb inequalities concerning multilinear integrals of products of functions in several dimensions. We give a complete treatment of the issues of finiteness of the constant, and of the existence and uniqueness of…
We study to what extent Lieb--Thirring inequalities are extendable from self-adjoint to general (possibly non-self-adjoint) Jacobi and Schr\"{o}dinger operators. Namely, we prove the conjecture of Hansmann and Katriel from [Complex Anal.…
We survey recent developments in the theory and applications of the broken ray transforms. Furthermore, we discuss some open problems.
We establish Lieb-Thirring power bounds on discrete eigenvalues of Jacobi operators for Schatten class complex perturbations of periodic and more generally finite gap Jacobi matrices.
We survey recent developments on the Restriction conjecture.
In this survey, we give a short overview of the recent progress on the multidimensional L2 conjecture. It can also serve as an introduction to the subject.
We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.
In this short note we present some remarks and conjectures on two of Erd\"os's open problems in number theory.
The aim of this paper is to present some new Fejer-type results for convex functions. Improvements of Young's inequality (the arithmetic-geometric mean inequality) and other applications to special means are pointed as well.
The paper contains a discussion on a number of open problems in queueing theory. Some of them are known for decades, some are more recent. They relate to stability and to rare events. There is an idea to prepare a special issue of QUESTA on…
Certain new inequalities for the sums of factorials are presented.
In this article we discuss a generalized Wirtinger inequality.
We consider some integral-geometric quantities that have recently arisen in harmonic analysis and elsewhere, derive some sharp geometric inequalities relating them, and place them in a wider context.
This paper presents an overview of the current state of knowledge in the field of equivariant map algebras and discusses some open problems in this area.