Zobrazeno 1 - 10
of 297
pro vyhledávání: '"Jørgensen, Palle E. T."'
The purpose of the present paper is to address multiple aspects of the Fuglede question dealing (Fourier spectra vs geometry) with a variety of $L^2$ contexts where we make precise the interplay between the three sides of the question: (i) existence
Externí odkaz:
http://arxiv.org/abs/2410.03587
Bratteli diagrams with countably infinite levels exhibit a new phenomenon: they can be horizontally stationary. The incidence matrices of these horizontally stationary Bratteli diagrams are infinite banded Toeplitz matrices. In this paper, we study t
Externí odkaz:
http://arxiv.org/abs/2409.10084
Autor:
Jorgensen, Palle E. T., Tian, James
Motivated by questions in quantum theory, we study Hilbert space valued Gaussian processes, and operator-valued kernels, i.e., kernels taking values in B(H) (= all bounded linear operators in a fixed Hilbert space H). We begin with a systematic study
Externí odkaz:
http://arxiv.org/abs/2408.10254
Autor:
Jorgensen, Palle E. T., Tian, James
We present a parallel between commutative and non-commutative polymorphisms. Our emphasis is the applications to conditional distributions from stochastic processes. In the classical case, both the measures and the positive definite kernels are scala
Externí odkaz:
http://arxiv.org/abs/2407.11846
Autor:
Jorgensen, Palle E. T., Tian, James
In the context of kernel optimization, we prove a result that yields new factorizations and realizations. Our initial context is that of general positive operator-valued kernels. We further present implications for Hilbert space-valued Gaussian proce
Externí odkaz:
http://arxiv.org/abs/2405.09315
Autor:
Jorgensen, Palle E. T., Tian, James
We offer new results and new directions in the study of operator-valued kernels and their factorizations. Our approach provides both more explicit realizations and new results, as well as new applications. These include: (i) an explicit covariance an
Externí odkaz:
http://arxiv.org/abs/2405.02796
Autor:
Jorgensen, Palle E. T., Tian, James
Motivated by applications, we introduce a general and new framework for operator valued positive definite kernels. We further give applications both to operator theory and to stochastic processes. The first one yields several dilation constructions i
Externí odkaz:
http://arxiv.org/abs/2404.14685
This paper introduces the concept of Fractal Frenet equations, a set of differential equations used to describe the behavior of vectors along fractal curves. The study explores the analogue of arc length for fractal curves, providing a measure to qua
Externí odkaz:
http://arxiv.org/abs/2404.07996
For multi-variable finite measure spaces, we present in this paper a new framework for non-orthogonal $L^2$ Fourier expansions. Our results hold for probability measures $\mu$ with finite support in $\mathbb{R}^d$ that satisfy a certain disintegratio
Externí odkaz:
http://arxiv.org/abs/2402.15950
Motivated by applications, we consider here new operator theoretic approaches to Conditional mean embeddings (CME). Our present results combine a spectral analysis-based optimization scheme with the use of kernels, stochastic processes, and construct
Externí odkaz:
http://arxiv.org/abs/2305.08100