Ilim ha’m ja’miyet Issue 2-1 (2026) · pp. 11-14

HARMONIC FUNCTIONS IN MATRIX SPACES

Xalknazarov, Askar Maxsetbaevich, Orazbekova, Dilbar Kosjanovna, Халкназаров, Аскар Махсетбаевич, Оразбекова, Дилбар Косжановна, Xalknazarov, Asqar Maxsetbaevich, Orazbekova, Dilbar Qosjan qızı

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Abstract

This paper investigates differential operators within the framework of matrix analysis. The definition of differential operators for matrix-valued functions, their matrix representation, and their invariant properties under linear fractional transformations are studied. Particular attention is paid to the generalized Laplace operator on matrix domains and its significance in the theory of harmonic functions.

matritsaviy analizdifferensial operatorLaplas operatoriinvariantlikmatritsaviy sohagarmonik funksiyaматричный анализдифференциальный оператороператор Лапласаинвариантность

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Cite

APA 7 
Xalknazarov, Askar Maxsetbaevich, Orazbekova, Dilbar Kosjanovna, Халкназаров, Аскар Махсетбаевич, Оразбекова, Дилбар Косжановна, Xalknazarov, Asqar Maxsetbaevich & Orazbekova, Dilbar Qosjan qızı (2026). HARMONIC FUNCTIONS IN MATRIX SPACES. Ilim ha’m ja’miyet, (2-1), 11-14.
GOST R 7.0.5 
Xalknazarov, Askar Maxsetbaevich, Orazbekova, Dilbar Kosjanovna, Халкназаров, Аскар Махсетбаевич, Оразбекова, Дилбар Косжановна, Xalknazarov, Asqar Maxsetbaevich, Orazbekova, Dilbar Qosjan qızı HARMONIC FUNCTIONS IN MATRIX SPACES // Ilim ha’m ja’miyet. 2026. № 2-1. С. 11-14.
BibTeX 
@article{maxsetbaevich2026,
  author  = {Xalknazarov, Askar Maxsetbaevich and Orazbekova, Dilbar Kosjanovna and Халкназаров, Аскар Махсетбаевич and Оразбекова, Дилбар Косжановна and Xalknazarov, Asqar Maxsetbaevich and Orazbekova, Dilbar Qosjan qızı},
  title   = {HARMONIC FUNCTIONS IN MATRIX SPACES},
  journal = {Ilim ha’m ja’miyet},
  year    = {2026},
  number  = {2-1},
  pages   = {11-14}
}
RIS 
TY  - JOUR
AU  - Xalknazarov, Askar Maxsetbaevich
AU  - Orazbekova, Dilbar Kosjanovna
AU  - Халкназаров, Аскар Махсетбаевич
AU  - Оразбекова, Дилбар Косжановна
AU  - Xalknazarov, Asqar Maxsetbaevich
AU  - Orazbekova, Dilbar Qosjan qızı
TI  - HARMONIC FUNCTIONS IN MATRIX SPACES
JO  - Ilim ha’m ja’miyet
PY  - 2026
IS  - 2-1
SP  - 11
EP  - 14
ER  -