相关论文: Tensor algebras and displacement structure. IV. In…
We study the structure of the inverse limit of the graded algebras of local unitary invariant polynomials using its Hilbert series. For k subsystems, we conjecture that the inverse limit is a free algebra and the number of algebraically…
We consider perturbations of dynamical semigroups on the algebra of all bounded operators in a Hilbert space generated by covariant completely positive measures on the semi-axis. The construction is based upon unbounded linear perturbations…
The structure of transformation semigroups on a finite set is analyzed by introducing a hierarchy of functions mapping subsets to subsets. The resulting hierarchy of semigroups has a corresponding hierarchy of minimal ideals, or kernels.…
We study the structure of the generator of a symmetric, conservative quantum dynamical semigroup with norm-bounded generator on a von Neumann algebra equipped with a faithful semifinite trace. For von Neumann algebras with abelian commutant…
We study how iterated and composed completely positive maps act on operator-valued kernels. Each kernel is realized inside a single Hilbert space where composition corresponds to applying bounded creation operators to feature vectors. This…
We study qualitative properties of the set of recurrent points of finitely generated free semigroups of measurable maps. In the case of a single generator the classical Poincare recurrence theorem shows that these properties are closely…
We study positive kernels on $X\times X$, where $X$ is a set equipped with an action of a group, and taking values in the set of $\mathcal A$-sesquilinear forms on a (not necessarily Hilbert) module over a $C^*$-algebra $\mathcal A$. These…
We define and study virtual representation spaces having both positive and negative dimensions at the vertices of a quiver without oriented cycles. We consider the natural semi-invariants on these spaces which we call virtual…
Kernel methods are powerful tools in machine learning. Classical kernel methods are based on positive-definite kernels, which map data spaces into reproducing kernel Hilbert spaces (RKHS). For non-Euclidean data spaces, positive-definite…
In this paper we explore the connection between tensor algebras and displacement structure. We describe a scattering experiment in this framework, we obtain a realization of the elements of the tensor algebra as transfer maps of a certain…
We investigate the interaction between the existence of reproducing kernels on infinite-dimensional Hermitian vector bundles and the positivity properties of the corresponding bundles. The positivity refers to the curvature form of certain…
We consider a semi-classical Dirac operator in arbitrary spatial dimensions with a smooth potential whose partial derivatives of any order are bounded by suitable constants. We prove that the distribution kernel of the inverse operator…
In this paper we study hermitian kernels invariant under the action of a semigroup with involution. We characterize those hermitian kernels which realize the given action by bounded operators on a Krein space. Applications to the GNS…
In this paper we continue to explore the connection between tensor algebras and displacement structure. We focus on recursive orthonormalization and we develop an analogue of the Szego type theory of orthogonal polynomials in the unit…
Given an algebra A, presented by generators and relations, i.e. as a quotient of a tensor algebra by an ideal, we construct a free algebra resolution of A, i.e. a differential graded algebra which is quasi-isomorphic to A and which is…
(2+1) dimensional diffusion equation is considered within the framework of equivalence transformations. Generators for the group are obtained and admissible transformations between linear and nonlinear equations are examined. It is shown…
For certain real quadratic number fields, we prove density results concerning 4-ranks of tame kernels. We also discuss a relationship between 4-ranks of tame kernels and 4-class ranks of narrow ideal class groups. Additionally, we give a…
We consider weakly positive semidefinite kernels valued in ordered $*$-spaces with or without certain topological properties, and investigate their linearisations (Kolmogorov decompositions) as well as their reproducing kernel spaces. The…
In this paper we establish individual ergodic theorem for positive kernels (or so called Danford Shwartz (DS+) operators acting on non commutative symmetric spaces.
We discuss a (i) quantized version of the Jordan decomposition theorem for a complex Borel measure on a compact Hausdorff space, namely, the more general problem of decomposing a general noncommutative kernel (a quantization of the standard…