Hilbert Space Decomposition Properties of Complex Functions and Their Applications

Authors

  • Myroslava I. Vovk Department of Advanced Mathematics, Lviv Polytechnic National University, Lviv 79000, Ukraine
  • Petro Ya. Pukach Department of Advanced Mathematics, Lviv Polytechnic National University, Lviv 79000, Ukraine
  • Volodymyr M. Dilnyi Department of Advanced Mathematics, Lviv Polytechnic National University, Lviv 79000, Ukraine
  • Anatolij K. Prykarpatski Department of Advanced Mathematics, Lviv Polytechnic National University, Lviv 79000, Ukraine

DOI:

https://doi.org/10.37256/cm.4420232386

Keywords:

decomposition, Bergman space, Hilbert space decomposition, Wold decomposition, invariant mapping, space invariance, ergodicity

Abstract

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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Published

2023-10-19

How to Cite

1.
Vovk MI, Pukach PY, Dilnyi VM, Prykarpatski AK. Hilbert Space Decomposition Properties of Complex Functions and Their Applications. Contemp. Math. [Internet]. 2023 Oct. 19 [cited 2024 May 28];4(4):702-9. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/2386