There is a recent and increasing interest in harmonic analysis of non-smooth geometries. Real-world examples where these types of geometry appear include large computer networks, relationships in datasets, and fractal structures such as those found in crystalline substances, light scattering, and other natural phenomena where dynamical systems are present. Notions of harmonic analysis focus on transforms and expansions and involve dual variables. In this book on smooth and non-smooth harmonic analysis, the notion of dual variables will be adapted to fractals. In addition to harmonic analysis via Fourier duality, the author also covers multiresolution wavelet approaches as well as a third tool, namely, L2 spaces derived from appropriate Gaussian processes. The book is based on a series of ten lectures delivered in June 2018 at a CBMS conference held at Iowa State University.
This volume consists of contributions spanning a wide spectrum of harmonic analysis and its applications written by speakers at the February Fourier Talks from 2002 – 2013.
The general aim of the present monograph is to study boundary-value problems for second-order elliptic operators in Lipschitz sub domains of Riemannian manifolds.
Ariel Barton and Svitlana Mayboroda Abstract Recent years have brought significant advances in the theory of higherorder elliptic equations in non-smooth domains. Sharp pointwise estimates on derivatives of polyharmonic functions in ...
This volume presents research and expository articles by the participants of the 25th Arkansas Spring Lecture Series on ``Recent Progress in the Study of Harmonic Measure from a Geometric and Analytic Point of View'' held at the University ...
Furthermore, as limiting objects in this theory are usually no more infinitely smooth, both differential geometry and ... Another co-centre of the book lies in the application of the modern analysis, in particular, harmonic analysis and ...
[1] [2] [3] [4] [5] [6] [7] [8] [10] [11] [12] [13] [14] References Pascal Auscher and Andreas Axelsson, Weighted maximal regularity estimates and solv- ability of non-smooth elliptic systems I, Invent. Math. 184 (2011), no.
... smooth local trigonometric bases, J. Fourier Anal. Appl. 2 (1995), 109-133. MR 1365201. [1995c] B. Jawerth and M. Mitrea, On the spectra of the higher-dimensional Maxwell operators on nonsmooth domains, in “Harmonic analysis and ...
Kenneth B. Howell. is a continuous function on (a, b). From part 3 we know | soda = X | voodo 0 k=1 **0 XXIV.(s) – W. (so)] k=1 = XXV (s) – XXV (so) = h(s) – h(so) k=1 k=1 So, s h(s) = h(so) + | g(o) do SO and h'6) = #160) #.
... there are so many important problems in materials science where Nature produces just such non-smooth boundaries. Conceptual developments in harmonic analysis are at the center of many important scientific and technological advances.
Krantz, S.G.: Integral formulas in complex analysis, in Bejing Lectures in Harmonic Analysis, Ann. of Math. Stud., vol. 112, pp. ... Krantz, S., Peloso, M.: The Bergman kernel and projection on non-smooth worm domains. Houst. J. Math.