Related papers: Spencer Operator and Applications: From Continuum …
The theory of symmetric, non-selfadjoint operators has several deep applications to the complex function theory of certain reproducing kernel Hilbert spaces of analytic functions, as well as to the study of ordinary differential operators…
The quantum mechanical commutation relations, which are directly related to the Heisenberg uncertainty principle, have a crucial importance for understanding the quantum mechanics of students. During undergraduate level courses, the…
The classical Arazy's decomposition theorem provides a powerful tool in the study of sequences in (and isomorphisms on) a separable operator ideal $\mathcal C_E$ of the algebra $\mathcal B(H)$ of all bounded linear operators on the…
Let S be the set of scalings 1, 2,3,4, ... and consider the corresponding set of scaled lattices in the plane. In this paper averaging operators are defined for plaquette functions on a lattice to plaquette functions on a coarser lattice…
We are concerned with the similarity problem for Cowen-Douglas operator tuples. The unitary equivalence counterpart was already investigated in the 1970's and geometric concepts including vector bundles and curvature appeared in the…
For linear operators which factor with suitable assumptions concerning commutativity of the factors, we introduce several notions of a decomposition. When any of these hold then questions of null space and range are subordinated to the same…
In 1960 Schwinger [J. Schwinger, Proc.Natl.Acad.Sci. 46 (1960) 570- 579] proposed the algorithm for factorization of unitary operators in the finite M dimensional Hilbert space according to a coprime decomposition of M. Using a special…
We start recalling with critical eyes the mathematical methods used in gauge theory and prove that they are not coherent with continuum mechanics, in particular the analytical mechanics of rigid bodies or hydrodynamics, though using the…
We introduce basic aspects of new operator method, which is very suitable for practical solving differential equations of various types. The main advantage of the method is revealed in opportunity to find compact exact operator solutions of…
This paper surveys the application of geometric algebra to the physics of electrons. It first appeared in 1996 and is reproduced here with only minor modifications. Subjects covered include non-relativistic and relativistic spinors, the…
Identifying a full basis of operators to a given order is key to the generality of Effective Field Theory (EFT) and is by now a problem of known solution in terms of the Hilbert series. The present work is concerned with hidden symmetry in…
Periodic Jacobi operators naturally arise in numerous applications, forming a cornerstone in various fields. The spectral theory associated with these operators boasts an extensive body of literature. Considered as discretized counterparts…
Operators play a substantial role in mathematical formalism of quantum mechanics. However, explicit forms of the operators are usually postulated, based on the intuitive assumptions. In this study, variational principle was applied to the…
After an historical introduction on the standard algebraic approach to quantum mechanics of large systems we review the basic mathematical aspects of the algebras of unbounded operators. After that we discuss in some details their relevance…
We show that the class of 1-exact operator systems is not uniformly definable by a sequence of types. We use this fact to show that there is no finitary version of Arveson's extension theorem. Next, we show that WEP is equivalent to a…
Let $\mathcal{M}$ be an atomless semifinite von Neumann algebra (or an atomic von Neumann algebra with all atoms having the same trace) acting on a (not necessarily separable) Hilbert space $H$ equipped with a semifinite faithful normal…
Paul Bernays and David Hilbert carefully avoided overspecification of Hilbert's epsilon-operator and axiomatized only what was relevant for their proof-theoretic investigations. Semantically, this left the epsilon-operator underspecified.…
The principle goal of computational mechanics is to define pattern and structure so that the organization of complex systems can be detected and quantified. Computational mechanics developed from efforts in the 1970s and early 1980s to…
The main aim of this book is to present recent results concerning inequalities for continuous functions of selfadjoint operators on complex Hilbert spaces. It is intended for use by both researchers in various fields of Linear Operator…
Our aim is to present several properties of a Landweber operator and of a Landweber-type operator. These operators are widely used in methods for solving the split feasibility problem and the split common fixed point problem. The presented…