Quasi-measures on the group G{sup m}, Dirichlet sets, and uniqueness problems for multiple Walsh series

Journal Article · Fri Feb 11 04:00:00 EST 2011 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2010V201N12ABEH004134; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21592580

Plotnikov, Mikhail G ^[1]

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1. Vologda State Academy of Milk Industry, Molochnoe, Vologda Region (Russian Federation)

Multiple Walsh series (S) on the group G{sup m} are studied. It is proved that every at most countable set is a uniqueness set for series (S) under convergence over cubes. The recovery problem is solved for the coefficients of series (S) that converge outside countable sets or outside sets of Dirichlet type. A number of analogues of the de la Vallee Poussin theorem are established for series (S). Bibliography: 28 titles.

• OSTI ID: 21592580
• Journal Information: Sbornik. Mathematics, Journal Name: Sbornik. Mathematics Journal Issue: 12 Vol. 201; ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
BOUNDARY-VALUE PROBLEMS
CONVERGENCE
DIRICHLET PROBLEM
GROUP THEORY
MATHEMATICS
MEASURE THEORY
SET THEORY