Displaying similar documents to “A factorization theorem in Banach lattices and its application to Lorentz spaces”

On some vector balancing problems

Apostolos Giannopoulos (1997)

Studia Mathematica

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Let V be an origin-symmetric convex body in ℝ n , n≥ 2, of Gaussian measure γ n ( V ) ≥ 1 / 2 . It is proved that for every choice u 1 , . . . , u n of vectors in the Euclidean unit ball B n , there exist signs ε j ∈ - 1 , 1 with ε 1 u 1 + . . . + ε n u n ∈ ( c l o g n ) V . The method used can be modified to give simple proofs of several related results of J. Spencer and E. D. Gluskin.

On an approximation property of Pisot numbers II

Toufik Zaïmi (2004)

Journal de Théorie des Nombres de Bordeaux

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Let q be a complex number, m be a positive rational integer and l m ( q ) = inf { P ( q ) , P ∈ ℤ m [ X ] , P ( q ) ≠ 0 } , where ℤ m [ X ] denotes the set of polynomials with rational integer coefficients of absolute value ≤ m . We determine in this note the maximum of the quantities l m ( q ) when q runs through the interval ] m , m + 1 [ . We also show that if q is a non-real number of modulus > 1 , then q is a complex Pisot number if and only if l m ( q ) > 0 for all m .

The ratio and generating function of cogrowth coefficients of finitely generated groups

Ryszard Szwarc (1998)

Studia Mathematica

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Let G be a group generated by r elements g 1 , … , g r . Among the reduced words in g 1 , … , g r of length n some, say γ n , represent the identity element of the group G. It has been shown in a combinatorial way that the 2nth root of γ 2 n has a limit, called the cogrowth exponent with respect to the generators g 1 , … , g r . We show by analytic methods that the numbers γ n vary regularly, i.e. the ratio γ 2 n + 2 / γ 2 n is also convergent. Moreover, we derive new precise information on the domain of holomorphy of γ(z), the generating function...

Extension of CR functions to «wedge type» domains

Andrea D'Agnolo, Piero D'Ancona, Giuseppe Zampieri (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let X be a complex manifold, S a generic submanifold of X R , the real underlying manifold to X . Let Ω be an open subset of S with ∂ ⁡ Ω analytic, Y a complexification of S . We first recall the notion of Ω -tuboid of X and of Y and then give a relation between; we then give the corresponding result in terms of microfunctions at the boundary. We relate the regularity at the boundary for ∂ ¯ b to the extendability of C ⁢ R functions on Ω to Ω -tuboids of X . Next, if X has complex dimension 2, we give results...

Polydisc slicing in ℂ n

Krzysztof Oleszkiewicz, Aleksander Pełczyński (2000)

Studia Mathematica

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Let D be the unit disc in the complex plane ℂ. Then for every complex linear subspace H in ℂ n of codimension 1, v o l 2 n - 2 ( D n - 1 ) ≤ v o l 2 n - 2 ( H ∩ D n ) ≤ 2 v o l 2 n - 2 ( D n - 1 ) . The lower bound is attained if and only if H is orthogonal to the versor e j of the jth coordinate axis for some j = 1,...,n; the upper bound is attained if and only if H is orthogonal to a vector e j + σ e k for some 1 ≤ j < k ≤ n and some σ ∈ ℂ with |σ| = 1. We identify ℂ n with ℝ 2 n ; by v o l k ( · ) we denote the usual k-dimensional volume in ℝ 2 n . The result is a complex counterpart of Ball’s [B1]...

On units of some fields of the form ℚ ( 2 , p , q , - l )

Mohamed Mahmoud Chems-Eddin (2023)

Mathematica Bohemica

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Let p ≡ 1 ( mod 8 ) and q ≡ 3 ( mod 8 ) be two prime integers and let ℓ ∉ { - 1 , p , q } be a positive odd square-free integer. Assuming that the fundamental unit of ℚ ( 2 p ) has a negative norm, we investigate the unit group of the fields ℚ ( 2 , p , q , - ℓ ) .