This unique book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. The book contains an unusually complete presentation of the Fourier transform calculus.
A developed, complete treatment of undergraduate probability and statistics by a very well known author. The approach develops a unified theory presented with clarity and economy. Included many examples and applications. Appropriate for an introductory undergraduate course in probability and statistics for students in engineering, math, the physical sciences, and computer science.(vs. Walpole/Myers, Miller/Freund, Devore, Scheaffer/McClave, Milton/Arnold)
Introduction to Fourier Analysis on Euclidean Spaces
The authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations, and to motivate the study of harmonic analysis on more general spaces having an analogous structure, e.g., symmetric spaces.
Local Cohomology: An Algebraic Introduction with Geometric ApplicationsThis book provides a careful and detailed algebraic introduction to Grothendieck's local cohomology theory, and illustrates many applications for the theory in commutative algebra and in the geometry of quasi-affine and quasi-projective varieties. Topics covered include Castelnuovo-Mumford regularity, the Fulton-Hansen connectedness theorem for projective varieties, and connections between local cohomology and both reductions of ideals and sheaf cohomology.
Pseudo Differential Operators & Markov Processes, Volume I
Volume 1: Fourier Analysis and Semigroups. Handles two topics in detail: Fourier analysis, with emphasis on positivity and also on some function spaces and multiplier theorems; and one parameter operator semigroups with emphasis on Feller semigroups and Lp-sub-Markovian semigroups. In addition, Dirichlet forms are treated.
