Some remarks on reproducing kernel Krein spaces

DOI10.1216/rmjm/1181072903zbMath0810.46025OpenAlexW1976084872MaRDI QIDQ1331454

Daniel Alpay

Publication date: 4 April 1995

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmjm/1181072903

zbMATH Keywords

reproducing kernel Hilbert spacespositive functionsreproducing kernel Krein spacesdifference of positive functions

Mathematics Subject Classification ID

Generalizations of inner products (semi-inner products, partial inner products, etc.) (46C50) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22)

Related Items (24)

A construction of unitary linear systems ⋮ Reproducing Kernel Kreĭn Spaces ⋮ Symmetry in tensor algebras over Hilbert space ⋮ Reflection positivity via Krein space analysis ⋮ Gleason's problem, rational functions and spaces of left-regular functions: the split-quaternion setting ⋮ Positive and generalized positive real lemma for slice hyperholomorphic functions ⋮ Matrices induced by arithmetic functions acting on certain Krein spaces ⋮ Herglotz functions: the Fueter variables case ⋮ Indefinite Proximity Learning: A Review ⋮ A construction of Krein spaces of analytic functions ⋮ Krein-space representations of arithmetic functions determined by primes ⋮ Asymptotic free probability for arithmetic functions and factorization of Dirichlet series ⋮ Some reproducing kernel spaces of continuous functions ⋮ Theory of subdualities ⋮ On linear combinations of positive functions, associated reproducing kernel spaces and a non Hermitian Schur algorithm ⋮ On L.\ Schwartz's boundedness condition for kernels ⋮ A theorem on reproducing kernel Hilbert spaces of pairs ⋮ Krein reproducing kernel modules in Clifford analysis ⋮ Representations of hermitian kernels by means of Kreĭn spaces ⋮ REPRESENTATIONS OF LIE ALGEBRAS BUILT OVER HILBERT SPACE ⋮ Realizations of holomorphic and slice hyperholomorphic functions: the Krein space case ⋮ A structure theorem for reproducing kernel Pontryagin spaces ⋮ Some extensions of Loewner's theory of monotone operator functions. ⋮ Supervised learning with indefinite topological Kernels

Cites Work

• Some Krein spaces of analytic functions and an inverse scattering problem
• On operator ranges
• Sous-espaces d'espaces vectoriels topologiques et noyaux associés. (Noyaux reproduisants.)
• Theory of Reproducing Kernels
• Perturbations of unitary transformations
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