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of 488
pro vyhledávání: '"Jorgensen, Palle E. T."'
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
We prove new factorization and dilation results for general positive operator-valued kernels, and we present their implications for associated Hilbert space-valued Gaussian processes, and their covariance structure. Further applications are to non-co
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