On mean value properties involving a logarithm-type weight

Nikolai G. Kuznecov

Mathematica Bohemica (2024)

  • Volume: 149, Issue: 3, page 419-425
  • ISSN: 0862-7959

Abstract

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Two new assertions characterizing analytically disks in the Euclidean plane ℝ 2 are proved. Weighted mean value property of positive solutions to the Helmholtz and modified Helmholtz equations are used for this purpose; the weight has a logarithmic singularity. The obtained results are compared with those without weight that were found earlier.

How to cite

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Kuznecov, Nikolai G.. "On mean value properties involving a logarithm-type weight." Mathematica Bohemica 149.3 (2024): 419-425. <http://eudml.org/doc/299491>.

@article{Kuznecov2024,
abstract = {Two new assertions characterizing analytically disks in the Euclidean plane $\mathbb \{R\}^2$ are proved. Weighted mean value property of positive solutions to the Helmholtz and modified Helmholtz equations are used for this purpose; the weight has a logarithmic singularity. The obtained results are compared with those without weight that were found earlier.},
author = {Kuznecov, Nikolai G.},
journal = {Mathematica Bohemica},
keywords = {harmonic function; Helmholtz equation; modified Helmholtz equation; mean value property; logarithmic weight; characterization of balls},
language = {eng},
number = {3},
pages = {419-425},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On mean value properties involving a logarithm-type weight},
url = {http://eudml.org/doc/299491},
volume = {149},
year = {2024},
}

TY - JOUR
AU - Kuznecov, Nikolai G.
TI - On mean value properties involving a logarithm-type weight
JO - Mathematica Bohemica
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 149
IS - 3
SP - 419
EP - 425
AB - Two new assertions characterizing analytically disks in the Euclidean plane $\mathbb {R}^2$ are proved. Weighted mean value property of positive solutions to the Helmholtz and modified Helmholtz equations are used for this purpose; the weight has a logarithmic singularity. The obtained results are compared with those without weight that were found earlier.
LA - eng
KW - harmonic function; Helmholtz equation; modified Helmholtz equation; mean value property; logarithmic weight; characterization of balls
UR - http://eudml.org/doc/299491
ER -

References

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  2. Evgrafov, M. A., Asymptotic Estimates and Entire Functions, Nauka, Moscow (1979), Russian. (1979) Zbl0447.30016MR0552276
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  8. Kuznetsov, N., 10.1007/s10958-022-06019-z, J. Math. Sci., New York 264 (2022), 603-608. (2022) Zbl1497.35109MR4466320DOI10.1007/s10958-022-06019-z
  9. Kuznetsov, N., 10.1090/spmj/1699, St. Petersbg Math. J. 33 (2022), 243-254. (2022) Zbl1485.35129MR4445758DOI10.1090/spmj/1699
  10. Kuznetsov, N., 10.1007/s10958-023-06254-y, J. Math. Sci., New York 269 (2023), 53-76. (2023) Zbl07676279MR4546947DOI10.1007/s10958-023-06254-y
  11. Kuznetsov, N., 10.1007/s10958-023-06323-2, J. Math. Sci., New York 269 (2023), 853-858. (2023) Zbl1536.31010MR4558666DOI10.1007/s10958-023-06323-2
  12. Netuka, I., 10.21136/CPM.1975.117893, Čas. Pěst. Mat. 100 (1975), 391-409 Czech. (1975) Zbl0314.31007MR0463461DOI10.21136/CPM.1975.117893
  13. Netuka, I., Veselý, J., Mean value property and harmonic functions, Classical and Modern Potential Theory and Applications NATO ASI Series, Ser. C: Mathematical and Physical Sciences 430. Kluwer Academic, Dordrecht (1994), 359-398. (1994) Zbl0863.31012MR1321628
  14. Nikiforov, A. F., Uvarov, V. B., 10.1007/978-1-4757-1595-8, Birkhäuser, Basel (1988). (1988) Zbl0624.33001MR0922041DOI10.1007/978-1-4757-1595-8

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