By Christopher D. Sogge
This complex monograph is anxious with glossy remedies of principal difficulties in harmonic research. the most subject of the e-book is the interaction among principles used to review the propagation of singularities for the wave equation and their opposite numbers in classical research. specifically, the writer makes use of microlocal research to check difficulties regarding maximal services and Riesz ability utilizing the so-called half-wave operator. to maintain the therapy self-contained, the writer starts with a quick evaluation of Fourier research and in addition develops the required instruments from microlocal research. This moment variation comprises new chapters. the 1st provides Hörmander's propagation of singularities theorem and makes use of this to end up the Duistermaat-Guillemin theorem. the second one issues more recent effects on the topic of the Kakeya conjecture, together with the maximal Kakeya estimates acquired through Bourgain and Wolff.
Read Online or Download Fourier Integrals in Classical Analysis (Cambridge Tracts in Mathematics) PDF
Best Abstract books
The current quantity completes the sequence of texts on algebra which the writer all started greater than ten years in the past. The account of box thought and Galois idea which we provide this is in keeping with the notions and result of basic algebra which look in our first quantity and at the extra straightforward components of the second one quantity, facing linear algebra.
During this variation, a collection of Supplementary Notes and comments has been additional on the finish, grouped in keeping with bankruptcy. a few of these name recognition to next advancements, others upload extra rationalization or extra feedback. many of the comments are followed via a in brief indicated facts, that is occasionally varied from the only given within the reference pointed out.
Geared toward moment yr graduate scholars, this article introduces them to cohomology thought (involving a wealthy interaction among algebra and topology) with at least necessities. No homological algebra is thought past what's as a rule discovered in a primary path in algebraic topology, and the fundamentals of the topic, in addition to workouts, are given sooner than dialogue of extra really good subject matters.
Following the elemental principles, ordinary structures and demanding examples within the concept of permutation teams, the booklet is going directly to strengthen the combinatorial and workforce theoretic constitution of primitive teams resulting in the facts of the pivotal ONan-Scott Theorem which hyperlinks finite primitive teams with finite easy teams.
Extra resources for Fourier Integrals in Classical Analysis (Cambridge Tracts in Mathematics)