This volume, the eighth out of nine, continues the translation of "Treatise on Analysis" by the French author and mathematician, Jean Dieudonne. The author shows how, for a voluntary restricted class of linear partial differential equations, the use of Lax/Maslov operators and pseudodifferential operators, combined with the spectral theory of operators in Hilbert spaces, leads to solutions that are much more explicit than solutions arrived at through "a priori" inequalities, which are useless applications.

Treatise on analysis / Vol. 3

Computers & Technology

Jean Dieudonné

Computer Science

Academic Press, New York, 1972

Foundations of Modern Analysis Volume 1

Science & Math

Earth Sciences

Academic Press

This book contains several fundamental ideas that are revived time after time in different guises, providing a better understanding of algebraic geometric phenomena. It shows how the field is enriched with loans from analysis and topology and from commutative algebra and homological algebra.

History of Algebraic Geometry

Mathematics

Chapman and Hall/CRC

This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincaré and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results.... Within its chosen boundaries the coverage of this book is superb. Read it! ―MathSciNet

A History of Algebraic and Differential Topology, 1900 - 1960

Birkhäuser Boston

Introduction Representations of $\mathbf {SU}(2)$ The general theory of linear representations of compact groups Lie theory of representations of compact connected Lie groups Induced representations of compact groups Spherical functions on compact groups Examples; spherical harmonics The general theory of spherical functions Fourier and Plancherel transforms Extension of the Plancherel transform The subtleties of harmonic analysis Differential properties of spherical functions on Lie groups Spherical functions on semisimple Lie groups More on $\mathbf {SL}(2, \mathbf R)$ Automorphic functions Groups of isometries and Bessel functions Other special functions References

Special Functions and Linear Representations of Lie Groups

American Mathematical Society

Infinitesimal Calculus

Kershaw Publishing Co Ltd

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Books by Jean Dieudonné