V. V. Volchkov, “Extremal cases of the Pompeiu problem”, Mat. Zametki, 59:5 (1996), 671–680; Math. Notes, 59:5 (1996), 482

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Matematicheskie Zametki, 1996, Volume 59, Issue 5, Pages 671–680
DOI: https://doi.org/10.4213/mzm1761 (Mi mzm1761)

This article is cited in 13 scientific papers (total in 13 papers)

Extremal cases of the Pompeiu problem

V. V. Volchkov

Donetsk National University

Full-text PDF (198 kB) Citations (13)

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DOI: https://doi.org/10.4213/mzm1761

Abstract: The Pompeiu problem is studied for functions defined on a ball $B\subset\mathbb R^n$ and having zero integrals over all sets congruent to a given compact set $K\subset B$. The problem of finding the least radius $r=r(K)$ of $B$ for which $K$ is a Pompeiu set is considered. The solution is obtained for the cases in which $K$ is a cube or a hemisphere.

Received: 01.10.1993

English version:
Mathematical Notes, 1996, Volume 59, Issue 5, Pages 482–489
DOI: https://doi.org/10.1007/BF02308814

Bibliographic databases:

UDC: 517

Language: Russian

Citation: V. V. Volchkov, “Extremal cases of the Pompeiu problem”, Mat. Zametki, 59:5 (1996), 671–680; Math. Notes, 59:5 (1996), 482–489

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm1761

https://doi.org/10.4213/mzm1761

https://www.mathnet.ru/eng/mzm/v59/i5/p671

This publication is cited in the following 13 articles:

V. V. Volchkov, “Local two-radii theorem in symmetric spaces”, Sb. Math., 198:11 (2007), 1553–1577
V. V. Volchkov, “Uniqueness theorems for solutions of the convolution equation on symmetric spaces”, Izv. Math., 70:6 (2006), 1077–1092
Vit. V. Volchkov, “Uniqueness Theorems for Periodic (in Mean) Functions on Quaternion Hyperbolic Space”, Math. Notes, 74:1 (2003), 30–37
Volchkov, VV, “Final version of the local two-radius theorem on the quaternion hyperbolic space”, Doklady Mathematics, 65:3 (2002), 389
V. V. Volchkov, “A definitive version of the local two-radii theorem on hyperbolic spaces”, Izv. Math., 65:2 (2001), 207–229
V. V. Volchkov, “Theorems on ball mean values in symmetric spaces”, Sb. Math., 192:9 (2001), 1275–1296
Volchkov, VV, “On functions with vanishing integrals over ellipsoids”, Doklady Mathematics, 63:1 (2001), 25
V. V. Volchkov, “Extremal problems on Pompeiu sets. II”, Sb. Math., 191:5 (2000), 619–632
Vit. V. Volchkov, “On functions with zero spherical means of complex hyperbolic spaces”, Math. Notes, 68:4 (2000), 436–443
Volchkov, VV, “On polyhedra with the local Pompeiu property”, Doklady Mathematics, 62:1 (2000), 69
V. V. Volchkov, “Injectivity sets of the Pompeiu transform”, Sb. Math., 190:11 (1999), 1607–1622
Volchkov, VV, “Functions with zero integrals over parallelepipeds”, Doklady Akademii Nauk, 369:4 (1999), 444
V. V. Volchkov, “Extremal problems on Pompeiu sets”, Sb. Math., 189:7 (1998), 955–976

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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References:	93
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