Operator-Related Function Theory and Time-Frequency by Karlheinz Gröchenig, Yurii Lyubarskii, Kristian Seip

By Karlheinz Gröchenig, Yurii Lyubarskii, Kristian Seip

This booklet collects the court cases of the 2012 Abel Symposium, held on the Norwegian Academy of technological know-how and Letters, Oslo. The Symposium, and this publication, are excited by vital fields of recent mathematical research: operator-related functionality conception and time-frequency research; and the profound interaction among them.

Among the unique contributions and evaluate lectures collected listed here are a paper offering multifractal research as a bridge among geometric degree conception and sign processing; neighborhood and worldwide geometry of Prony platforms and Fourier reconstruction of piecewise-smooth features;  Bernstein's challenge on weighted polynomial approximation; singular distributions and symmetry of the spectrum; and plenty of others.

Offering a range of the most recent and most enjoyable effects acquired by way of world-leading researchers, the publication will gain scientists operating in Harmonic and intricate research, Mathematical Physics and sign Processing.

Show description

Read Online or Download Operator-Related Function Theory and Time-Frequency Analysis: The Abel Symposium 2012 (Abel Symposia) PDF

Best theory books

Computer Aided Systems Theory – EUROCAST 2011: 13th International Conference, Las Palmas de Gran Canaria, Spain, February 6-11, 2011, Revised Selected Papers, Part II

The two-volume lawsuits, LNCS 6927 and LNCS 6928, represent the papers offered on the thirteenth foreign convention on computing device Aided platforms conception, EUROCAST 2011, held in February 2011 in Las Palmas de Gran Canaria, Spain. the whole of a hundred and sixty papers awarded have been rigorously reviewed and chosen for inclusion within the books.

Stochastic Theory and Control: Proceedings of a Workshop held in Lawrence, Kansas

This quantity comprises just about all of the papers that have been offered on the Workshop on Stochastic thought and keep watch over that was once held on the Univ- sity of Kansas, 18–20 October 2001. This three-day occasion accrued a gaggle of prime students within the ? eld of stochastic conception and keep an eye on to debate modern subject matters of stochastic keep an eye on, which come with hazard delicate keep watch over, adaptive keep an eye on, arithmetic of ?

Papers in Honour of Bernhard Banaschewski: Proceedings of the BB Fest 96, a Conference Held at the University of Cape Town, 15–20 July 1996, on Category Theory and its Applications to Topology, Order and Algebra

Bobbing up from the 1996 Cape city convention in honour of the mathematician Bernhard Banaschewski, this number of 30 refereed papers represents present advancements in class conception, topology, topos thought, common algebra, version conception, and various ordered and algebraic constructions. Banaschewski's impression is mirrored the following, quite within the contributions to pointfree topology on the degrees of nearness, uniformity, and asymmetry.

Additional resources for Operator-Related Function Theory and Time-Frequency Analysis: The Abel Symposium 2012 (Abel Symposia)

Example text

1 such that 2. x0 / Ä 2. H C"/jn I (53) let Dj D f W 2. H "/j Ä d Ä 2. C1 H C"/j g A Bridge Between Geometric Measure Theory and Signal Processing:. . 41 Let now ı > 0 be fixed. H / C 2ı; so that "; H C "/ Ä 2. H /C2ı/j : Therefore Dj is covered by 2. H / C 2ı: Since this estimate holds for any ı > 0, the first upper bound is proved. We now turn to the second bound in Theorem 5. We first assume that the support of f is a closed interval of the form ŒHmin ; Hmax . H // Ä 2. H // covers ŒHmin ; Hmax .

Proposition 3. e. A/ D 1). A/ 1=C . Proof. Let fBi g be an arbitrary "-covering of A. Bi / Ä C jBi jı : Bi Ä The result follows by passing to the limit when " ! 0. As an example of application of Proposition 3, let us derive a lower bound for the dimension of K. l1 /ı ; (26) so that, by (25), m0 C m1 D 1. lik /ı D jI jı : 18 P. Abry et al. I / Ä jI jı . Let J be the void interval of smallest generation included in I . J 0 /. 1 l0 l1 /ı jJ jı Ä C 0 jI jı : The mass distribution principle therefore implies that dim K obtained the following result.

It can also be used for exponents of different nature, see for instance [3, 44] where the exponent considered is the size of ergodic averages, or [4, 20] where it is the rate of divergence of Fourier series. In Sect. 1 we will give an easy example in such an alternative setting: We will consider the rate of divergence of the wavelet series of a function in a given Sobolev or Besov space. It follows that, for a given function, several notions of pointwise exponents can be considered, leading to different notions of multifractal spectra.

Download PDF sample

Rated 4.96 of 5 – based on 3 votes
This entry was posted in Theory.