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By Elias M. Stein,Rami Shakarchi

This is the fourth and ultimate quantity within the Princeton Lectures in research, a chain of textbooks that target to give, in an built-in demeanour, the center components of research. starting with the elemental evidence of useful research, this quantity seems to be at Banach areas, Lp areas, and distribution conception, and highlights their roles in harmonic research. The authors then use the Baire class theorem to demonstrate a number of issues, together with the lifestyles of Besicovitch units. the second one half the e-book introduces readers to different important issues in research, akin to chance idea and Brownian movement, which culminates within the answer of Dirichlet's challenge. The concluding chapters discover a number of advanced variables and oscillatory integrals in Fourier research, and illustrate purposes to such various parts as nonlinear dispersion equations and the matter of counting lattice issues. in the course of the e-book, the authors specialize in key leads to every one sector and rigidity the natural cohesion of the subject.

  • A entire and authoritative textual content that treats many of the major themes of recent research
  • A examine simple sensible research and its functions in harmonic research, chance conception, and several other advanced variables
  • Key leads to every one quarter mentioned on the subject of different parts of arithmetic
  • Highlights the natural cohesion of huge components of research characteristically break up into subfields
  • Interesting workouts and difficulties illustrate principles
  • Clear proofs provided

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Functional Analysis: Introduction to Further Topics in Analysis: Bk. 4 (Princeton Lectures in Analysis) by Elias M. Stein,Rami Shakarchi

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