Problems and Theorems in Analysis I

Front Cover
Springer Science & Business Media, Dec 11, 1997 - Mathematics - 389 pages
1 Review
From the reviews: "The work is one of the real classics of this century; it has had much influence on teaching, on research in several branches of hard analysis, particularly complex function theory, and it has been an essential indispensable source book for those seriously interested in mathematical problems. These volumes contain many extraordinary problems and sequences of problems, mostly from some time past, well worth attention today and tomorrow. Written in the early twenties by two young mathematicians of outstanding talent, taste, breadth, perception, perseverence, and pedagogical skill, this work broke new ground in the teaching of mathematics and how to do mathematical research. (Bulletin of the American Mathematical Society)
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Selected pages

Contents

Infinite Series and Infinite Sequences
1
Linear Transformations of Series A Theorem of Cesŕro
15
The Structure of Real Sequences and Series
23
Miscellaneous Problems
32
Integration
46
Inequalities
62
Some Properties of Real Functions
75
Various Types of Equidistribution
85
Functions of Large Numbers
95
Functions of One Complex Variable General Part
103
Mappings and Vector Fields
113
Some Geometrical Aspects of Complex Variables
125
Cauchys Theorem The Argument Principle
133
Sequences of Analytic Functions
145
The Maximum Principle
157
Copyright

Common terms and phrases

References to this book

All Book Search results »

About the author (1997)

Biography of George Pólya

Born in Budapest, December 13, 1887, George Pólya initially studied law, then languages and literature in Budapest. He came to mathematics in order to understand philosophy, but the subject of his doctorate in 1912 was in probability theory and he promptly abandoned philosophy.
After a year in Göttingen and a short stay in Paris, he received an appointment at the ETH in Zürich. His research was multi-faceted, ranging from series, probability, number theory and combinatorics to astronomy and voting systems. Some of his deepest work was on entire functions. He also worked in conformal mappings, potential theory, boundary value problems, and isoperimetric problems in mathematical physics, as well as heuristics late in his career. When Pólya left Europe in 1940, he first went to Brown University, then two years later to Stanford, where he remained until his death on September 7, 1985.


Biography of Gabor Szegö

Born in Kunhegyes, Hungary, January 20, 1895, Szegö studied in Budapest and Vienna, where he received his Ph. D. in 1918, after serving in the Austro-Hungarian army in the First World War. He became a privatdozent at the University of Berlin and in 1926 succeeded Knopp at the University of Kšnigsberg. It was during his time in Berlin that he and Pólya collaborated on their great joint work, the Problems and Theorems in Analysis. Szegö's own research concentrated on orthogonal polynomials and Toeplitz matrices. With the deteriorating situation in Germany at that time, he moved in 1934 to Washington University, St. Louis, where he remained until 1938, when he moved to Stanford. As department head at Stanford, he arranged for Pólya to join the Stanford faculty in 1942. Szegö remained at Stanford until his death on August 7, 1985.