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Mat. Zametki, 1998, Volume 63, Issue 1, Pages 69–80 (Mi mz1249)  

This article is cited in 21 scientific papers (total in 21 papers)

On the total variation for functions of several variables and a multidimensional analog of Helly's selection principle

A. S. Leonov

Moscow Engineering Physics Institute (State University)

Abstract: We introduce the new notion of total variation for the Hardy class of functions of several variables and state various properties, similar to those in the one-dimensional case, for functions belonging to this class. In particular, we prove a precise version of Helly's selection principle for this class.

DOI: https://doi.org/10.4213/mzm1249

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English version:
Mathematical Notes, 1998, 63:1, 61–71

Bibliographic databases:

UDC: 517.397
Received: 22.04.1996

Citation: A. S. Leonov, “On the total variation for functions of several variables and a multidimensional analog of Helly's selection principle”, Mat. Zametki, 63:1 (1998), 69–80; Math. Notes, 63:1 (1998), 61–71

Citation in format AMSBIB
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\jour Math. Notes
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Leonov, AS, “Numerical piecewise-uniform regularization for two-dimensional ill-posed problems”, Inverse Problems, 15:5 (1999), 1165  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    2. A. S. Leonov, “Primenenie funktsii neskolkikh peremennykh s ogranichennymi variatsiyami dlya chislennogo resheniya dvumernykh nekorrektnykh zadach”, Sib. zhurn. vychisl. matem., 2:3 (1999), 257–271  mathnet  zmath
    3. Chistyakov, VV, “Superposition operators in the algebra of functions of two variables with finite total variation”, Monatshefte fur Mathematik, 137:2 (2002), 99  crossref  mathscinet  zmath  isi  scopus  scopus
    4. Balcerzak, M, “On Helly's principle for metric semigroup valued by mappings of two real variables”, Bulletin of the Australian Mathematical Society, 66:2 (2002), 245  crossref  mathscinet  zmath  isi
    5. V. V. Chistyakov, “Abstract superposition operators on mappings of bounded variation of two real variables. I”, Siberian Math. J., 46:3 (2005), 555–571  mathnet  crossref  mathscinet  zmath  isi  elib
    6. Chistyakov, VV, “A Banach algebra of functions of several variables of finite total variation and Lipschitzian superposition operators. II”, Nonlinear Analysis-Theory Methods & Applications, 63:1 (2005), 1  crossref  mathscinet  zmath  isi  scopus  scopus
    7. Chistyakov, VV, “A Banach algebra of functions of several variables of finite total variation and Lipschitzian superposition operators. I”, Nonlinear Analysis-Theory Methods & Applications, 62:3 (2005), 559  crossref  mathscinet  zmath  isi  scopus
    8. Kohl, N, “Evolving neural networks for strategic decision-making problems”, Neural Networks, 22:3 (2009), 326  crossref  mathscinet  isi  elib  scopus  scopus
    9. Chistyakov V.V., Tretyachenko Yu.V., “Maps of Several Variables of Finite Total Variation. I. Mixed Differences and the Total Variation”, J. Math. Anal. Appl., 370:2 (2010), 672–686  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    10. Chistyakov V.V., Tretyachenko Yu.V., “Maps of Several Variables of Finite Total Variation. II. E. Helly-Type Pointwise Selection Principles”, J. Math. Anal. Appl., 369:1 (2010), 82–93  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    11. Chistyakov V.V., Tretyachenko Yu.V., “Selection Principles for Maps of Several Variables”, Dokl. Math., 81:2 (2010), 282–285  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    12. A. S. Leonov, “Higher-order total variations for functions of several variables and their application in the theory of ill-posed problems”, Proc. Steklov Inst. Math. (Suppl.), 280, suppl. 1 (2013), 119–133  mathnet  crossref  isi  elib
    13. Bantsuri L.D., Oniani G.G., “On Differential Properties of Functions of Bounded Variation”, Anal. Math., 38:1 (2012), 1–17  crossref  mathscinet  zmath  isi
    14. Lind M., “Estimates of the Total P-Variation of Bivariate Functions”, J. Math. Anal. Appl., 401:1 (2013), 218–231  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    15. Chistyakov V.V., Tretyachenko Yu.V., “A Pointwise Selection Principle for Maps of Several Variables via the Total Joint Variation”, J. Math. Anal. Appl., 402:2 (2013), 648–659  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    16. Aziz W., Leiva H., Merentes N., “Solutions of Hammerstein Equations in the Space $BV (I_a^b)$”, Quaest. Math., 37:3 (2014), 359–370  crossref  mathscinet  zmath  isi  scopus  scopus
    17. Aistleitner Ch., Dick J., “Functions of Bounded Variation, Signed Measures, and a General Koksma-Hlawka Inequlity”, Acta Arith., 167:2 (2015), 143–171  crossref  mathscinet  zmath  isi
    18. Aistleitner Ch., Pausinger F., Svane A.M., Tichy R.F., “On functions of bounded variation”, Math. Proc. Camb. Philos. Soc., 162:3 (2017), 405–418  crossref  mathscinet  zmath  isi  scopus
    19. Chistyakov V.V., Chistyakova S.A., “Pointwise Selection Theorems For Metric Space Valued Bivariate Functions”, J. Math. Anal. Appl., 452:2 (2017), 970–989  crossref  mathscinet  zmath  isi  scopus  scopus
    20. Radulovic D., Wegkamp M., Zhao Yu., “Weak Convergence of Empirical Copula Processes Indexed By Functions”, Bernoulli, 23:4B (2017), 3346–3384  crossref  mathscinet  zmath  isi  scopus  scopus
    21. Bracamonte M., Ereu J., Gimenez J., Merentes N., “On Metric Semigroups-Valued Functions of Bounded Riesz-Phi-Variation in Several Variables”, Bol. Soc. Mat. Mex., 24:1 (2018), 133–153  crossref  mathscinet  zmath  isi
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