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Necessary conditions for the Fourier coefficients of periodic functions to belong to B(p, $θ$ k, $α$ )-classes of Besov type.

Beriša, M. (1984)

Publications de l'Institut Mathématique. Nouvelle Série

Necessary conditions for the $L^{p}$ -convergence $(0 < p < 1)$ of single and double trigonometric series

Xhevat Z. Krasniqi, Péter Kórus, Ferenc Móricz (2014)

Mathematica Bohemica

We give necessary conditions in terms of the coefficients for the convergence of a double trigonometric series in the $L^{p}$ -metric, where $0 < p < 1$ . The results and their proofs have been motivated by the recent papers of A. S. Belov (2008) and F. Móricz (2010). Our basic tools in the proofs are the Hardy-Littlewood inequality for functions in $H^{p}$ and the Bernstein-Zygmund inequalities for the derivatives of trigonometric polynomials and their conjugates in the $L^{p}$ -metric, where $0 < p < 1$ .

Negative values of cosine sums

Imre Z. Ruzsa (2004)

Acta Arithmetica

Newer applications of generalized monotone sequences.

Leindler, Laszlo (2006)

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

Nombres de Pisot et fonctions moyenne-périodiques

François Gramain (1974/1975)

Séminaire Delange-Pisot-Poitou. Théorie des nombres

Nonconvolution transforms with oscillating kernels that map $Ḃ_{1}^{0, 1}$ into itself

G. Sampson (1993)

Studia Mathematica

We consider operators of the form $(Ω f) (y) = ʃ_{- \infty}^{\infty} Ω (y, u) f (u) d u$ with Ω(y,u) = K(y,u)h(y-u), where K is a Calderón-Zygmund kernel and $h \in L^{\infty}$ (see (0.1) and (0.2)). We give necessary and sufficient conditions for such operators to map the Besov space $Ḃ_{1}^{0, 1}$ (= B) into itself. In particular, all operators with $h (y) = e^{{i | y |}^{a}}$ , a > 0, a ≠ 1, map B into itself.

Nonlinear Approximation Theory on Compact Groups.

K.-L. Kueh, T. Olson, D. Rockmore (2001)

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

Nonmonotone nonconvolution functions of positive type and applications

Tomáš Bárta (2012)

Commentationes Mathematicae Universitatis Carolinae

We present two sufficient conditions for nonconvolution kernels to be of positive type. We apply the results to obtain stability for one-dimensional models of chemically reacting viscoelastic materials.

Nonperiodic Sampling of Bandlimited Functions on Unions of Rectangular Lattices.

David Walnut (1995)

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

Norm convergence of some power series of operators in $L^{p}$ with applications in ergodic theory

Christophe Cuny (2010)

Studia Mathematica

Let X be a closed subspace of $L^{p} (μ)$ , where μ is an arbitrary measure and 1 < p < ∞. Let U be an invertible operator on X such that $s u p_{n \in ℤ} | | U ⁿ | | < \infty$ . Motivated by applications in ergodic theory, we obtain (optimal) conditions for the convergence of series like $\sum_{n \geq 1} (U ⁿ f) / n^{1 - α}$ , 0 ≤ α < 1, in terms of $| | f + \dots + U^{n - 1} f {| |}_{p}$ , generalizing results for unitary (or normal) operators in L²(μ). The proofs make use of the spectral integration initiated by Berkson and Gillespie and, more particularly, of results from a paper by Berkson-Bourgain-Gillespie....

Notes on integral transformations [Book]

Paweł Szeptycki (1984)

Notiz zu dem Aufsatze: Beweis, dass eine für jeden reellen Werth von x durch eine trigonometrische Reihe gegebene Function f(x) sich nur auf eine einzige Weise in dieser Form darstellen lässt. Bd. 72, Seite 139

G. Cantor (1871)

Journal für die reine und angewandte Mathematik

Numerical Computation of the Fourier Transform Using Laguerre Functions and the Fast Fourier Transform.

H. Weber (1980/1981)

Numerische Mathematik

Currently displaying 1 – 16 of 16