On the Dynamics of Matrix Models for Immune Clonal Networks

Balinsky, Alexander; Gafiychuk, V. V.; Kyshakevych, B. Yu.; Prykarpatsky, Anatoliy K.

doi:10.1007/s10958-022-05920-x

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Main Invariant Decomposition Results and Examples1

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2023

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“…A D being finite dimensional, makes it possible to generate an infinite hierarchy of ergodic matrix valued mappings, widely used in modern quantum computer science [32,33], neural networks [34,35], and artificial intelligence [36][37][38] studies.…”

Section: Main Invariant Decomposition Results and Examplesmentioning

confidence: 99%

Hilbert Space Decomposition Properties of Complex Functions and Their Applications

Vovk,

Pukach,

Dilnyi

et al. 2023

Contemp. Math.

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We analyzed the classical problem of decomposing the Hilbert space of holomorphic functions, especially their splitting into the product or sum of domain-separated components. For the Bergman space of analytical functions, we obtained a special decomposition satisfying the assigned growth degree properties. Concerning a general Hilbert space of analytical functions on a connected domain, we studied its α-invariant decomposition and related ergodic consequences. As an interesting consequence, we obtained the decomposition theorem for an ergodic α-mapping on the Bergman space of holomorphic functions.

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