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We consider hilbert spaces of holomorphic functions in Cartan domains (in particular in ball and polydisk) and operator of restriction of holomorphic function to a submanifold in Shilov boundary. We discuss conditions when this operator…
The study of spectral graph determination is a fascinating area of research in spectral graph theory and algebraic combinatorics. This field focuses on examining the spectral characterization of various classes of graphs, developing methods…
In this paper we show that, for a class of countable graphs, every representation of the associated graph algebra in a separable Hilbert space is unitarily equivalent to a representation obtained via branching systems.
We consider a large class of self-adjoint elliptic problem associated with the second derivative acting on a space of vector-valued functions. We present two different approaches to the study of the associated eigenvalues problems. The…
In statistical learning theory, interpolation spaces of the form $[\mathrm{L}^2,H]_{\theta,r}$, where $H$ is a reproducing kernel Hilbert space, are in widespread use. So far, however, they are only well understood for fine index $r=2$. We…
In this paper spectral theorems for not necessarily continuous normal and self-adjoint random operators on a complex separable Hilbert space are proved.
We show that the Hilbert functor of points on an arbitrary separated algebraic stack is an algebraic space. We also show the algebraicity of the Hilbert stack of points on an algebraic stack and the algebraicity of the Weil restriction of…
In this paper we study differentiability properties of the map $T\mapsto\phi(T)$, where $\phi$ is a given function in the disk-algebra and $T$ ranges over the set of contractions on Hilbert space. We obtain sharp conditions (in terms of…
A holographic description of scalar mesons is presented, in which two- and three-point functions are holographically reconstructed. Mass spectrum, decay constants, eigenfunctions and the coupling of the scalar states with two pseu-…
New identities on traces of representations of the Hecke algebra on the spaces of paths on graphs are presented. These identities are relevant in the computation of partition functions with fixed boundary conditions and of two-point…
The decomposition into interaction subspaces is an important result for graphical models and plays a central role for results on the linearized marginal problem; similarly the Chaos decomposition plays an important role in statistical…
The geometric Langlands program is distinguished in assigning spectral decompositions to all representations, not only the irreducible ones. However, it is not even clear what is meant by a spectral decomposition when one works with…
The relationship between locality graphs and deconstruction hierarchies of conformal models is explained, leading to computationally effective procedures for determining the latter, and the relevant notions are illustrated with several…
The mathematics underlying the connection between deconstruction lattices and locality diagrams of conformal models is developed from scratch, with special emphasis on classification issues. In particular, the notions of equilocality…
We are interested in the general question: to what extent are the spectral properties of a graph connected to the distance function? Our motivation is a concrete example of this question that is due to Steinerberger. We provide some…
The concept of local fractional derivative was introduced in order to be able to study the local scaling behavior of functions. However it has turned out to be much more useful. It was found that simple equations involving these operators…
We develop a holomorphic functional calculus for (multivalued linear) operators on locally convex vector spaces. This includes the case of fractional powers along Lipschitz curves.
We give a Herglotz-type representation of an arbitrary generalized spectral measure. As an application, a new proof of the classical Naimark's dilation theorem is given. The same approach is used to describe the spectrum of all unitary…
Analysis of function spaces and special functions are closely related to the representation theory of Lie groups. We explain here the connection between the Laguerre functions, the Laguerre polynomials, and the Meixner-Pollacyck polynomials…
In this paper, we propose a simple but effective method for fast image segmentation. We re-examine the locality-preserving character of spectral clustering by constructing a graph over image regions with both global and local connections.…