The logarithmic capacity in
S. Kołodziej (1988)
Annales Polonici Mathematici
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S. Kołodziej (1988)
Annales Polonici Mathematici
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Alexander Koldobsky, Marisa Zymonopoulou (2003)
Studia Mathematica
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We study the extremal volume of central hyperplane sections of complex n-dimensional -balls with 0 < p ≤ 2. We show that the minimum corresponds to hyperplanes orthogonal to vectors ξ = (ξ¹,...,ξⁿ) ∈ ℂⁿ with |ξ¹| = ... = |ξⁿ|, and the maximum corresponds to hyperplanes orthogonal to vectors with only one non-zero coordinate.
Leokadia Bialas-Ciez (2012)
Annales Polonici Mathematici
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The paper is concerned with the best constants in the Bernstein and Markov inequalities on a compact set . We give some basic properties of these constants and we prove that two extremal-like functions defined in terms of the Bernstein constants are plurisubharmonic and very close to the Siciak extremal function . Moreover, we show that one of these extremal-like functions is equal to if E is a nonpluripolar set with where , the supremum is taken over all polynomials P of N variables...
B. Platynowicz (1980)
Matematički Vesnik
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Gerd Herzog, Peer Chr. Kunstmann (2015)
Commentationes Mathematicae Universitatis Carolinae
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We prove the existence of functions , the Fourier series of which being universally divergent on countable subsets of . The proof is based on a uniform estimate of the Taylor polynomials of Landau’s extremal functions on .
T. Bloom, N. Levenberg, S. Ma'u (2003)
Annales Polonici Mathematici
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Given a compact set , for each positive integer n, let = := sup: p holomorphic polynomial, 1 ≤ deg p ≤ n. These “extremal-like” functions are essentially one-variable in nature and always increase to the “true” several-variable (Siciak) extremal function, := max[0, sup1/(deg p) log|p(z)|: p holomorphic polynomial, ]. Our main result is that if K is regular, then all of the functions are continuous; and their associated Robin functions increase to for all z outside a pluripolar...
Amitabha Tripathi (2008)
Czechoslovak Mathematical Journal
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Let be fixed positive integers, and let be any set of positive integers. Let denote the set of all integers representable as a sum of no more than elements of , and let denote the largest integer such that . Let , where the maximum is taken over all sets with elements. We determine when the elements of are in geometric progression. In particular, this results in the evaluation of and yields surprisingly sharp lower bounds for , particularly for .
Lucjan Siewierski
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CONTENTSIntroduction...............................................................................................................................................................................5Definitions and notation.........................................................................................................................................................7The main result........................................................................................................................................................................91....
Xi Guo and Lan Wu (2015)
Communications in Mathematics
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Let be an -dimensional submanifold in the unit sphere , we call a -extremal submanifold if it is a critical point of the functional . In this paper, we can study gap phenomenon for these submanifolds.
Scott Duke Kominers, Zachary Abel (2008)
Journal de Théorie des Nombres de Bordeaux
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We show that if is an extremal even unimodular lattice of rank with , then is generated by its vectors of norms and . Our result is an extension of Ozeki’s result for the case .