Abstract
In this paper we obtain recovery formulas for coefficients of multiple Ciesielski series by means of its sum, if the square partial sums of a Ciesielski series converge in measure to a function \(f\) and the majorant of partial sums satisfies some necessary condition.
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REFERENCES
A. B. Aleksandrov, ‘‘A-integrability of the boundary values of harmonic functions,’’ Math. Notes Acad. Sci. USSR 30, 515–523 (1981). https://doi.org/10.1007/BF01158819
Ph. Franklin, ‘‘A set of continuous orthogonal functions,’’ Math. Ann. 522–528 (1928). https://doi.org/10.1515/9781400827268.189
G. G. Gevorkyan, ‘‘Uniqueness of Franklin series,’’ Math. Notes Acad. Sci. USSR 46, 609–615 (1989). https://doi.org/10.1007/BF01137624
G. G. Gevorkyan, ‘‘On the uniqueness of trigonometric series,’’ Math. USSR Sb. 68, 325–338 (1991). https://doi.org/10.1070/SM1991v068n02ABEH002107
G. G. Gevorkyan, ‘‘On uniqueness of additive functions of dyadic cubes and series by Haar systems,’’ J. Contemp. Math. Anal. 30, 2–13 (1995).
G. G. Gevorkyan and K. A. Navasardyan, ‘‘On Haar series of A-integrable functions,’’ J. Contemp. Math. Anal. 52, 149–160 (2017). https://doi.org/10.3103/S1068362317030062
G. G. Gevorkyan and M. P. Poghosyan, ‘‘On recovering of coefficients of Franklin series with a ‘‘good’’ majorant of partial sums,’’ J. Contemp. Math. Anal. 52 254–260 (2017). https://doi.org/10.3103/S1068362317050053
G. G. Gevorkyan, ‘‘Uniqueness theorem for multiple Franklin series,’’ Math. Notes 101, 219–229 (2017). https://doi.org/10.1134/S0001434617010266
G. G. Gevorkyan, K. A. Keryan, and M. P. Poghosyan, ‘‘Convergence to infinity for orthonormal spline series,’’ Acta Math. Hung. 162, 604–617 (2020). https://doi.org/10.1007/s10474-020-01051-4
B. S. Kashin and A. A. Sahakyan, Orthogonal Series (AFTs, Moscow, 1999; AMS, Providence, RI, 2005).
K. A. Keryan, ‘‘A uniqueness theorem for Franklin series,’’ J. Contemp. Math. Anal. 52, 92–101 (2017). https://doi.org/10.3103/S1068362317020054
V. V. Kostin, ‘‘Reconstructing coefficients of series from certain orthogonal systems of functions,’’ Math. Notes 73, 662–679 (2003). https://doi.org/10.1023/A:1024012705318
K. A. Navasardyan, ‘‘Uniqueness theorems for multiple Franklin series,’’ Proc. Yerevan State Univ., Phys. Math. Sci. 51, 241–249 (2017).
K. A. Navasardyan, ‘‘On a uniqueness theorem for the Franklin system,’’ Proc. Yerevan State Univ., Phys. Math. Sci. 52, 93–100 (2018).
W. Böhm, ‘‘Inserting new knots into B-spline curves,’’ Comput.-Aided Des. 12, 199–201 (1980). https://doi.org/10.1016/0010-4485(80)90154-2
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Khachatryan, A. A Uniqueness Theorem for Multiple Orthonormal Spline Series. J. Contemp. Mathemat. Anal. 56, 118–127 (2021). https://doi.org/10.3103/S1068362321030043
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DOI: https://doi.org/10.3103/S1068362321030043