R. A. Bashmakov, K. P. Isaev, R. S. Yulmukhametov, “On geometric characteristics of convex functions and Laplace integrals”, Ufa Math. J., 2:1 (2010)

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Ufimskii Matematicheskii Zhurnal, 2010, Volume 2, Issue 1, Pages 3–16 (Mi ufa38)

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

On geometric characteristics of convex functions and Laplace integrals

R. A. Bashmakov^a, K. P. Isaev^a, R. S. Yulmukhametov^b

^a Bashkir State University, Ufa, Russia
^b Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa, Russia

Full-text PDF (430 kB) Citations (13)

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Abstract: In many problems of analysis the second derivatives are used to characterize the convexity of the function that imposes serious restrictions on a class of considered functions. This paper introduces the geometric characteristics of convexity, which from our point of view are more natural in the study of weighted spaces of functions. In the one-dimensional case, the problem is considered in more detail and we define the various characteristics, which are in a sense equivalent. As an application we study the asymptotic behavior of multidimensional Laplace integral.

Keywords: convex functions, Young's conjugate function, Laplace transform.

Received: 20.02.2010

Bibliographic databases:

Document Type: Article

UDC: 517.54

Language: Russian

Citation: R. A. Bashmakov, K. P. Isaev, R. S. Yulmukhametov, “On geometric characteristics of convex functions and Laplace integrals”, Ufa Math. J., 2:1 (2010)

Citation in format AMSBIB

\Bibitem{BasIsaYul10}

\by R.~A.~Bashmakov, K.~P.~Isaev, R.~S.~Yulmukhametov

\paper On geometric characteristics of convex functions and Laplace integrals

\jour Ufa Math. J.

\yr 2010

\vol 2

\issue 1

\mathnet{http://mi.mathnet.ru/eng/ufa38}

\zmath{https://zbmath.org/?q=an:1240.26026}

Linking options:

https://www.mathnet.ru/eng/ufa38

https://www.mathnet.ru/eng/ufa/v2/i1/p3

This publication is cited in the following 13 articles:

K. P. Isaev, R. S. Yulmukhametov, “Unconditional bases in radial Hilbert spaces”, Izv. Math., 86:1 (2022), 150–168
R. S. Yulmukhametov, “Dual spaces for weighted spaces of locally integrable functions”, Ufa Math. J., 13:4 (2021), 112–122
K. P. Isaev, R. S. Yulmukhametov, “Equivalent conditions for the existence of unconditional bases of reproducing kernels in spaces of entire functions”, Probl. anal. Issues Anal., 10(28):3 (2021), 41–52
K. P. Isaev, R. S. Yulmukhametov, “Geometry of radial Hilbert spaces with unconditional bases of reproducing kernels”, Ufa Math. J., 12:4 (2020), 55–63
I. Kh. Musin, “On A Certain Class of Entire Functions”, J. Math. Sci. (N. Y.), 252:3 (2021), 428–435
I. Kh. Musin, “On a Hilbert space of entire functions”, Ufa Math. J., 9:3 (2017), 109–117
K. P. Isaev, R. S. Yulmukhametov, “On unconditional bases of reproducing kernels in Fock-type spaces”, Funct. Anal. Appl., 51:4 (2017), 283–292
Isaev K.P., “On Unconditional Exponential Bases in Weighted Spaces on Interval of Real Axis”, Lobachevskii J. Math., 38:1 (2017), 48–61
K. P. Isaev, A. V. Lutsenko, R. S. Yulmukhametov, “On unconditional exponential bases in weak weighted spaces on segment”, Ufa Math. J., 8:4 (2016), 88–97
K. P. Isaev, R. S. Yulmukhametov, A. A. Yunusov, “On unconditional exponential bases in weighted spaces on interval of real axis”, St. Petersburg Math. J., 28:5 (2017), 689–706
R. A. Bashmakov, A. A. Makhota, K. V. Trounov, “On absence conditions of unconditional bases of exponents”, Ufa Math. J., 7:2 (2015), 17–32
A. A. Yunusov, “On unconditional exponential bases in weighted spaces on real axis”, Ufa Math. J., 7:3 (2015), 108–118
K. P. Isaev, R. S. Yulmukhametov, “Unconditional exponential bases in Hilbert spaces”, Ufa Math. J., 3:1 (2011), 3–15

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

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