Cross theorem for separately real-analytic functions Cross theorem for separately real-analytic functions

The present work is devoted to the study of R -analyticity with respect to the set of variables of separately R -analytic functions. In the paper, it is proved real analyticity with respect to the set of variables, out of some pluripolar set, of the separately R -analytic functions.

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Bibliographic Details
Published in:The Journal of Analysis Vol. 33; no. 5; pp. 2413 - 2420
Main Authors: Alimardon, Atamuratov, Kamol, Rasulov
Format: Journal Article
Language:English
Published: Singapore Springer Nature Singapore 01.10.2025
Springer Nature B.V
Subjects:
Abstract Harmonic Analysis
Analysis
Fourier Analysis
Functional Analysis
Mathematics
Mathematics and Statistics
Measure and Integration
Neighborhoods
Original Research Paper
Special Functions
Variables
32D10
measure
analytic function
32A10
26E05
Pluripolar set
32U35
Regular point
ISSN:0971-3611, 2367-2501
Online Access:Get full text
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Summary:The present work is devoted to the study of R -analyticity with respect to the set of variables of separately R -analytic functions. In the paper, it is proved real analyticity with respect to the set of variables, out of some pluripolar set, of the separately R -analytic functions.
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content type line 14
ISSN:0971-3611
2367-2501
DOI:10.1007/s41478-025-00942-5