Zeros of Random Functions Generated with de Branges Kernels

We study the point process given by the set of real zeros of random series generated with orthonormal bases of reproducing kernels of de Branges spaces. We find an explicit formula for the intensity function in terms of the phase of the Hermite-Biehler function generating the de Branges space. We pr...

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Detalles Bibliográficos
Autores principales: Antezana, Jorge Abel, Marzo, Jordi, Olsen, Jan-Fredrik
Formato: Articulo
Lenguaje:Inglés
Publicado: 2017
Materias:
Matemática
Gaussian analytic functions
De Branges spaces
First intensity function
Kac-rice formula
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/102363
https://ri.conicet.gov.ar/11336/20214
https://academic.oup.com/imrn/article-abstract/2017/8/2284/3060657/Zeros-of-Random-Functions-Generated-with-de
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
Descripción
Sumario:We study the point process given by the set of real zeros of random series generated with orthonormal bases of reproducing kernels of de Branges spaces. We find an explicit formula for the intensity function in terms of the phase of the Hermite-Biehler function generating the de Branges space. We prove that the intensity of the point process completely characterizes the underlying de Branges space.

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