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A two-sided sequence ${(c ₙ)}_{n \in ℤ}$ with values in a complex unital Banach algebra is a cosine sequence if it satisfies $c_{n + m} + c_{n - m} = 2 c ₙ c ₘ$ for any n,m ∈ ℤ with c₀ equal to the unity of the algebra. A cosine sequence ${(c ₙ)}_{n \in ℤ}$ is bounded if $s u p_{n \in ℤ} | | c ₙ | | < \infty$ . A (bounded) group decomposition for a cosine sequence $c = {(c ₙ)}_{n \in ℤ}$ is a representation of c as $c ₙ = (b ⁿ + b^{- n}) / 2$ for every n ∈ ℤ, where b is an invertible element of the algebra (satisfying $s u p_{n \in ℤ} | | b ⁿ | | < \infty$ , respectively). It is known that every bounded cosine sequence possesses a universally defined group decomposition, here referred...

On Hardy spaces in complex ellipsoids

Thomas Hansson (1999)

Annales de l'institut Fourier

This paper deals with atomic decomposition and factorization of functions in the holomorphic Hardy space $H^{1}$ . Such representation theorems have been proved for strictly pseudoconvex domains. The atomic decomposition has also been proved for convex domains of finite type. Here the Hardy space was defined with respect to the ordinary Euclidean surface measure on the boundary. But for domains of finite type, it is natural to define $H^{1}$ with respect to a certain measure that degenerates near Levi-flat points...

On harmonic conjugates with exponential mean growth

Miroslav Pavlović (1999)

Czechoslovak Mathematical Journal

On Hartman almost periodic functions

Guy Cohen, Viktor Losert (2006)

Studia Mathematica

We consider multi-dimensional Hartman almost periodic functions and sequences, defined with respect to different averaging sequences of subsets in $ℝ^{d}$ or $ℤ^{d}$ . We consider the behavior of their Fourier-Bohr coefficients and their spectrum, depending on the particular averaging sequence, and we demonstrate this dependence by several examples. Extensions to compactly generated, locally compact, abelian groups are considered. We define generalized Marcinkiewicz spaces based upon arbitrary measure spaces...

On Heisenberg and local uncertainty principles for the $q$ -Dunkl transform.

Fitouhi, Ahmed, Nouri, Ferjani, Guesmi, Sana (2009)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

On Hermite expansion of $x_{+}^{p}$

Zbigniew Sadlok (1980)

Annales Polonici Mathematici

On High Precision Methods for the Evaluation of Fourier Integrals with Finite and Infinite Limits.

T.N.L. Patterson (1976/1977)

Numerische Mathematik

On Higher Riesz Transforms for Gaussian Measures.

C.E. Gutiérrez, C. Segovia (1995)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

On holomorphy in Banach spaces and absolute convergence of Fourier series

Matos, Mário C. (1988)

Portugaliae mathematica

On infinitely smooth almost-wavelets with compact support.

M. Berkolaiko, I. Novikov (1993)

Collectanea Mathematica

There are known wavelets with exponential decay on infinity [2,3,4] and wavelets with compact support [5]. But these functions have finite smoothness. It is known that there do not exist infinitely differentiable compactly supported wavelets.

On instances of Fox’s integral equation connection to the Riemann zeta function

Alexander E. Patkowski (2019)

Archivum Mathematicum

We consider some applications of the singular integral equation of the second kind of Fox. Some new solutions to Fox’s integral equation are discussed in relation to number theory.

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Displaying 141 – 160 of 561

On fractional derivatives

On general Franklin systems [Book]

On General Hermite Trigonometric Interpolation.

On generalized Jacobi matrices and orthogonal polynomials.

On generation and propagation of tsunamis in a shallow running ocean.

On group decompositions of bounded cosine sequences