Open AccessReproducing Kernel in Krein Spaces
Author(s) -
Osmin Ferrer,
Diego Carrillo,
Arnaldo de la Barrera
Publication year - 2022
Publication title -
wseas transactions on mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.211
H-Index - 21
eISSN - 2224-2880
pISSN - 1109-2769
DOI - 10.37394/23206.2022.21.4
Subject(s) - kernel (algebra) , mathematics , reproducing kernel hilbert space , hilbert space , kernel embedding of distributions , subspace topology , representer theorem , pure mathematics , bergman kernel , context (archaeology) , positive definite matrix , variable kernel density estimation , metric (unit) , kernel principal component analysis , space (punctuation) , algebra over a field , kernel method , mathematical analysis , artificial intelligence , computer science , eigenvalues and eigenvectors , support vector machine , physics , paleontology , operations management , quantum mechanics , economics , biology , operating system
This article describes a new form to introduce a reproducing kernel for a Krein space based on orthogonal projectors enabling to describe the kernel of a Krein space as the difference between the kernel of definite positive subspace and the kernel of definite negative subspace corresponding to kernel of the associated Hilbert space. As application, the authors obtain some basic properties of both kernels for Krein spaces and exhibit that each kernel is uniquely determined by the Krein space given. The methods and results employed generalize the notion of reproducing kernel given in Hilbert spaces to the context of spaces endowed with indefinite metric.