Related papers: Higher-Order-Schmidt-Representations and their Rel…
We study a version of the functional Hodrick-Prescott filter where the associated operator is not necessarily compact, but merely closed and densely defined with closed range. We show that the associated optimal smoothing operator preserves…
The higher spin Laplace operator has been constructed recently as the generalization of the Laplacian in higher spin theory. This acts on functions taking values in arbitrary irreducible representations of the Spin group. In this paper, we…
The sets of contexts and properties of a concept are embedded in the complex Hilbert space of quantum mechanics. States are unit vectors or density operators, and contexts and properties are orthogonal projections. The way calculations are…
This paper compares different representations (in the sense of computable analysis) of a number of function spaces that are of interest in analysis. In particular subspace representations inherited from a larger function space are compared…
The generalized q-deformed valence-bond-solid groundstate of one-dimensional higher integer spin model is studied. The Schwinger boson representation and the matrix product representation of the exact groundstate is determined, which…
Several classes of irreducible orthogonal representations of compact Lie groups that are of importance in Differential Geometry have the property that the second osculating spaces of all of their nontrivial orbits coincide with the…
We show how to construct relevant families of matrix product operators in one and higher dimensions. Those form the building blocks for the numerical simulation methods based on matrix product states and projected entangled pair states. In…
A notion of stratification is introduced for any compactly generated triangulated category T endowed with an action of a graded commutative noetherian ring R. The utility of this notion is demonstrated by establishing diverse consequences…
In this paper, we study the inner product of states corresponding to weights of finite-dimensional highest-weight representations of classical groups. We prove that the action of the raising operators would reduce a state of hight-weight…
The purpose of the present paper is to lay the foundations for a systematic study of tensor products of operator systems. After giving an axiomatic definition of tensor products in this category, we examine in detail several particular…
We extend the matrix representation of magnetic pseudo-differential operators in a tight Gabor frame from [arXiv:1804.05220, arXiv:2212.12229] to asymmetrical quantizations and smooth symbols dominated by a tempered weight (and not just…
This talk is devoted mainly to the concept of higher-order polarization on a group, which is introduced in the framework of a Group Approach to Quantization, as a powerful tool to guarantee the irreducibility of quantizations and/or…
We construct a class of representations of the Heisenberg algebra in terms of the complex shift operators subject to the proper continuous limit imposed by the correspondence principle. We find a suitable Hilbert space formulation of our…
We discuss the polar in symbol space to hypoelliptic and partially hypoelliptic operators, assuming a transmission property related to a rectifiable boundary and using a representation based on two scalar products.
For a semibounded sesquilinear form ${\mathfrak t}$ in a Hilbert space ${\mathfrak H}$ there exists a representing map $Q$ from ${\mathfrak H}$ to another Hilbert space ${\mathfrak K}$, such that ${\mathfrak t}[\varphi, \psi]-c(\varphi,…
All compact $AC(\sigma)$ operators have a representation analogous to that for compact normal operators. As a partial converse we obtain conditions which allow one to construct a large number of such operators. Using the results in the…
In this work, we prove that any element in the tensor product of separable infinite-dimensional Hilbert spaces can be expressed as a matrix product state (MPS) of possibly infinite bond dimension. The proof is based on the singular value…
A representation field for a non-maximal order $\Ha$ in a central simple algebra is a subfield of the spinor class field of maximal orders which determines the set of spinor genera of maximal orders containing a copy of $\Ha$. Not every…
We provide a recipe for building explicit representations of the real Clifford algebras once an explicit family is given in dimensions $1$ through $4$. We further give an explicit construction of spin coordinate systems for a given real…
For a connected semisimple algebraic group $G$, we consider some special infinite series of tensor products of simple $G$-modules whose $G$-fixed point spaces are at most one-dimensional. We prove that their existence is closely related to…