相关论文: Three open problems in analysis

We present a treasure trove of open problems in matrix and operator inequalities, of a functional analytic nature, and with various degrees of hardness.

In this paper, an open problem in the multidimensional complex analysis is pesented that arises in the investigation of the regularity properties of Fourier integral operators and in the regularity theory for hyperbolic partial differential…

In this paper some open problems for Painlev\'e equations are discussed. In particular the following open problems are described: (i) the Painlev\'e equivalence problem; (ii) notation for solutions of the Painlev\'e equations; (iii)…

A list of open problems in the field of analysis of boolean functions, compiled February 2012 for the Simons Symposium.

The light field reconstruction from the focal stack can be mathematically formulated as an ill-posed integral equation inversion problem. Although the previous research about this problem has made progress both in practice and theory, its…

We present and discuss seven different open problems in applied combinatorics. The application areas relevant to this compilation include quantum computing, algorithmic differentiation, topological data analysis, iterative methods,…

We discuss several open problems on spectrally bounded operators, some new, some old, adding in a few new insights.

We study the inversion of the conical Radon which integrates a function in three-dimensional space from integrals over circular cones. The conical Radon recently got significant attention due to its relevance in various imaging applications…

In this paper we consider three types of discrete operators stemming from singular Radon transforms. We first extend an $\ell^p$ result for translation invariant discrete singular Radon transforms to a class of twisted operators including…

In the present article we consider the uniqueness problem for the generalized Radon transform arising in a mathematical model of production. We prove uniqueness theorems for this transform and for the profit function in the corresponding…

We continue to study the problem of modeling of substitution of production factors motivated by the need for computable mathematical models of economics that could be used as a basis in applied developments. This problem has been studied…

In this thesis we study three problems. The first is the superposition of the operators and their proprities, such as boundedness,continuity,regularity and the inequalities of the norms of the composition of functions in some functional…

We describe a list of open problems in random matrix theory and the theory of integrable systems that was presented at the conference Asymptotics in Integrable Systems, Random Matrices and Random Processes and Universality, Centre de…

We discuss various problems in frame theory that have been open for some years. A short discussion of frame theory is also provided, but it only contains the information that is necessary in order to understand the open problems and their…

The aim of this paper is to share with the mathematical community a list of 33 problems that I have found along the years during my research. I believe that it is worth to think about them and, hopefully, it will be possible either to solve…

The monograph contains a systematic treatment of a circle of problems in analysis and integral geometry related to inversion of the Radon transform on the space of real rectangular matrices. This transform assigns to a function $f$ on the…

We present 35 open problems on combinatorial, geometric and algebraic aspects of k-orbit abstract polytopes. We also present a theory of rooted polytopes that has appeared implicitly in previous work but has not been formalized before.

This is a survey on algorithmic questions about combinatorial and geometric properties of convex polytopes. We give a list of 35 problems; for each the current state of knowledege on its theoretical complexity status is reported. The…

In this thesis, the numerical solution of three different classes of problems have been studied. Specifically, new techniques have been proposed and their theoretical analysis has been performed, accompanied by a wide set of numerical…

Generalizing Lemma 28 from Newton's ``Principia", Arnold asked for a complete characterization of algebraically integrable domains. In this paper we describe the current state of Arnold's problems. We also consider closely related problems…