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3 papers
Extremal functions of integral functionals in $H^\omega[a,b]$
S. K. Bagdasarov Ohio State University
Abstract:
In this paper we give a solution of the discrete and continuous versions of the problem
$$
\int_a^bh(t)\psi(t)\,dt\to\sup, \quad h\in H^\omega[a,b]\colon\quad h(a)=E_1, \quad h(b)=E_2,
$$
where
$H^\omega[a,b]$ is the class of absolutely continuous functions on
$[a,b]$ with common majorizing modulus of continuity
$\omega$. We also discuss applications of the results obtained to mathematical economics (the Kantorovich–Monge mass transfer problem), approximation theory and numerical differentiation (Chebyshev
$\omega$-polynomials and splines), the constructive theory of functions (inequalities for
$\omega$-rearrangements), graph theory (graphs of rearrangements), and optimal control theory (the theory of total control and the Fel'dbaum–Bushaw problem).
MSC: 49J30,
41A17 Received: 27.11.1997
DOI:
10.4213/im241
Fulltext:
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