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Ideal norms and trigonometric orthonormal systems

Jörg Wenzel (1994)

Studia Mathematica

We characterize the UMD-property of a Banach space X by sequences of ideal norms associated with trigonometric orthonormal systems. The asymptotic behavior of those numerical parameters can be used to decide whether X is a UMD-space. Moreover, if this is not the case, we obtain a measure that shows how far X is from being a UMD-space. The main result is that all described sequences are not only simultaneously bounded but are also asymptotically equivalent.

Idele characters in spectral synthesis on 𝐑 / 2 π 𝐙

John J. Benedetto (1973)

Annales de l'institut Fourier

Let s C , x R / 2 π Z . We construct Dirichlet series F ( x , x ) where for each fixed s in a half plane, Re F ( x , x ) , as a function of x , is a non-synthesizable absolutely convergent Fourier series. Because of the way the frequencies in F are chosen, we are motivated to introduce a class of synthesizable absolutely convergent Fourier series which are defined in terms of idele characters. We solve the “problem of analytic continuation” in this setting by constructing pseudo-measures, determined by idele characters, when Re s 1 .

Idempotents in quotients and restrictions of Banach algebras of functions

Thomas Vils Pedersen (1996)

Annales de l'institut Fourier

Let 𝒜 β be the Beurling algebra with weight ( 1 + | n | ) β on the unit circle 𝕋 and, for a closed set E 𝕋 , let J 𝒜 β ( E ) = { f 𝒜 β : f = 0 on a neighbourhood of E } . We prove that, for β > 1 2 , there exists a closed set E 𝕋 of measure zero such that the quotient algebra 𝒜 β / J 𝒜 β ( E ) is not generated by its idempotents, thus contrasting a result of Zouakia. Furthermore, for the Lipschitz algebras λ γ and the algebra 𝒜 𝒞 of absolutely continuous functions on 𝕋 , we characterize the closed sets E 𝕋 for which the restriction algebras λ γ ( E ) and 𝒜 𝒞 ( E ) are generated by their idempotents.

Identification of basic thermal technical characteristics of building materials

Stanislav Šťastník, Jiří Vala, Hana Kmínová (2007)

Kybernetika

Modelling of building heat transfer needs two basic material characteristics: heat conduction factor and thermal capacity. Under some simplifications these two factors can be determined from a rather simple equipment, generating heat from one of two aluminium plates into the material sample and recording temperature on the contacts between the sample and the plates. However, the numerical evaluation of both characteristics leads to a non-trivial optimization problem. This article suggests an efficient...

Images of Gaussian random fields: Salem sets and interior points

Narn-Rueih Shieh, Yimin Xiao (2006)

Studia Mathematica

Let X = X ( t ) , t N be a Gaussian random field in d with stationary increments. For any Borel set E N , we provide sufficient conditions for the image X(E) to be a Salem set or to have interior points by studying the asymptotic properties of the Fourier transform of the occupation measure of X and the continuity of the local times of X on E, respectively. Our results extend and improve the previous theorems of Pitt [24] and Kahane [12,13] for fractional Brownian motion.

Images of some functions and functional spaces under the Dunkl-Hermite semigroup

Néjib Ben Salem, Walid Nefzi (2013)

Commentationes Mathematicae Universitatis Carolinae

We propose the study of some questions related to the Dunkl-Hermite semigroup. Essentially, we characterize the images of the Dunkl-Hermite-Sobolev space, 𝒮 ( ) and L α p ( ) , 1 < p < , under the Dunkl-Hermite semigroup. Also, we consider the image of the space of tempered distributions and we give Paley-Wiener type theorems for the transforms given by the Dunkl-Hermite semigroup.

In a shadow of the RH: Cyclic vectors of Hardy spaces on the Hilbert multidisc

Nikolai Nikolski (2012)

Annales de l’institut Fourier

Completeness of a dilation system ( ϕ ( n x ) ) n 1 on the standard Lebesgue space L 2 ( 0 , 1 ) is considered for 2-periodic functions ϕ . We show that the problem is equivalent to an open question on cyclic vectors of the Hardy space H 2 ( 𝔻 2 ) on the Hilbert multidisc 𝔻 2 . Several simple sufficient conditions are exhibited, which include however practically all previously known results (Wintner; Kozlov; Neuwirth, Ginsberg, and Newman; Hedenmalm, Lindquist, and Seip). For instance, each of the following conditions implies cyclicity...

Inclusion relations between harmonic Bergman-Besov and weighted Bloch spaces on the unit ball

Ömer Faruk Doğan, Adem Ersin Üreyen (2019)

Czechoslovak Mathematical Journal

We consider harmonic Bergman-Besov spaces b α p and weighted Bloch spaces b α on the unit ball of n for the full ranges of parameters 0 < p < , α , and determine the precise inclusion relations among them. To verify these relations we use Carleson measures and suitable radial differential operators. For harmonic Bergman spaces various characterizations of Carleson measures are known. For weighted Bloch spaces we provide a characterization when α > 0 .

Indefinite integration of oscillatory functions

Paweł Keller (1998)

Applicationes Mathematicae

A simple and fast algorithm is presented for evaluating the indefinite integral of an oscillatory function x y i f ( t ) e i ω t d t , -1 ≤ x < y ≤ 1, ω ≠ 0, where the Chebyshev series expansion of the function f is known. The final solution, expressed as a finite Chebyshev series, is obtained by solving a second-order linear difference equation. Because of the nature of the equation special algorithms have to be used to find a satisfactory approximation to the integral.

Indices of Orlicz spaces and some applications

Alberto Fiorenza, Miroslav Krbec (1997)

Commentationes Mathematicae Universitatis Carolinae

We study connections between the Boyd indices in Orlicz spaces and the growth conditions frequently met in various applications, for instance, in the regularity theory of variational integrals with non-standard growth. We develop a truncation method for computation of the indices and we also give characterizations of them in terms of the growth exponents and of the Jensen means. Applications concern variational integrals and extrapolation of integral operators.

Inégalités à poids pour l'opérateur de Hardy-Littlewood-Sobolev dans les espaces métriques mesurés à deux demi-dimensions

David Mascré (2006)

Colloquium Mathematicae

On a metric measure space (X,ϱ,μ), consider the weight functions w α ( x ) = ϱ ( x , z ) - α if ϱ(x,z₀) < 1, w α ( x ) = ϱ ( x , z ) - α if ϱ(x,z₀) ≥ 1, w β ( x ) = ϱ ( x , z ) - β if ϱ(x,z₀) < 1, w β ( x ) = ϱ ( x , z ) - β if ϱ(x,z₀) ≥ 1, where z₀ is a given point of X, and let κ a : X × X be an operator kernel satisfying κ a ( x , y ) c ϱ ( x , y ) a - d for all x,y ∈ X such that ϱ(x,y) < 1, κ a ( x , y ) c ϱ ( x , y ) a - D for all x,y ∈ X such that ϱ(x,y)≥ 1, where 0 < a < min(d,D), and d and D are respectively the local and global volume growth rate of the space X. We determine conditions on a, α₀, α₁, β₀, β₁ ∈ ℝ for the Hardy-Littlewood-Sobolev operator...

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