Related papers: Six problems in frame theory
This is a short introduction to Hilbert space frame theory and its applications for those outside the area who want to enter the subject. We will emphasize finite frame theory since it is the easiest way to get into the subject.
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 we review many interesting open problems in mathematical physics which may be attacked with the help of tools from constructive field theory. They could give work for future mathematical physicists trained with the…
This paper first describes, from a high level viewpoint, the main challenges that had to be solved in order to develop a theory of spin glasses in the last fifty years. It then explains how important inference problems, notably those…
This is a brief review of the present status, of some recent developments and of the open challenges in string/M theory.
Frame theory is recently an active research area in mathematics, computer science and engineering with many exciting applications in a variety of different fields. This theory has been generalized rapidly and various generalizations of…
Fifteen years after their discovery, ample fields now stand at the center of research in contemporary Galois theory and attract more and more attention also from other areas of mathematics. This survey gives an introduction to the theory of…
In this survey article we discuss key open problems which could serve as a guidance for further research directions of multiplicative ideal theory and factorization theory.
Students' difficulties in quantum mechanics may be the result of unproductive framing and not a fundamental inability to solve the problems or misconceptions about physics content. We observed groups of students solving quantum mechanics…
In this paper we discuss some topics related to the general theory of frames. In particular we focus our attention to the existence of different 'reconstruction formulas' for a given vector of a certain Hilbert space and to some refinement…
We discuss some open problems in a program of constructing and studying two-dimensional conformal field theories using the representation theory of vertex operator algebras.
Since it first emerged in Wijsman's seminal work [29], the Wijsman topology has been intensively studied in the past 50 years. In particular, topological properties of Wijsman hyperspaces, relationships between the Wijsman topology and…
Frame theory is an exciting, dynamic and fast paced subject with applications in numerous fields of mathematics and engineering. In this paper we study Continuous Frame and introduce Continuous Frame with $C^{\ast}$-valued bounds. Also, we…
A selection of open problems in the theory of composites is presented. Particular attention is drawn to the question of whether two-dimensional, two-phase, composites with general geometries have the same set of possible effective tensors…
The topic of the glass transition gives rise to a a wide diversity of views. It is, accordingly, characterized by a lack of agreement on which would be the most profitable theoretical perspective. In this chapter, I provide some elements…
An assessment of the present status of the theory, some immediate tasks which are suggested thereby and some questions whose answers may require a longer breath since they relate to significant changes in the conceptual and mathematical…
A general theory of frames of reference proposed in a preceding publication is considered here in the framework of the post-Newtonian approximation, assuming that the frame of reference is centered on a time-like geodesic. The problem of…
When we discuss problems on gravity, we can not avoid some fundamental physical problems, such as space-time, inertia, and inertial reference frame. The goal of this paper is to discuss the logic system of gravity theory and the problems of…
In this chapter we survey two topics that have recently been investigated in frame theory. First, we give an overview of the class of scalable frames. These are (finite) frames with the property that each frame vector can be rescaled in…
In this expository paper, I survey Room frames and Kirkman frames, concentrating on the early history of these objects. I mainly look at the basic construction techniques, but I also provide some historical remarks and discussion. I also…