InequalitiesCambridge University Press, 1952 - 324 pagine This classic of the mathematical literature forms a comprehensive study of the inequalities used throughout mathematics. First published in 1934, it presents clearly and lucidly both the statement and proof of all the standard inequalities of analysis. The authors were well-known for their powers of exposition and made this subject accessible to a wide audience of mathematicians. |
Sommario
INTRODUCTION | 1 |
4647 | 43 |
MEAN VALUES WITH AN ARBITRARY | 65 |
9 | 75 |
INFINITE SERIES | 114 |
Miscellaneous theorems and examples | 124 |
SOME APPLICATIONS OF | 172 |
SOME THEOREMS CONCERNING | 196 |
1 | 227 |
Thorins proof and extension | 306 |
Altre edizioni - Visualizza tutto
Inequalities Godfrey Harold Hardy,John Edensor Littlewood,George Pólya Visualizzazione estratti - 1964 |
Parole e frasi comuni
a₁ a₂ ambn argument asserts best possible bilinear Calculus of Variations consider constant continuous and strictly convergent convex function corresponding curve deduce Theorem deduced from Theorem defined definition denote effectively proportional equality equation example F₁ finite number follows from Theorem Fourier Fourier series generalisations Hardy and Littlewood Hence Hilbert's Hölder's inequality homogeneous i₁ increasing function infinite interval Lebesgue Lebesgue integrals maximum means monotonic functional multilinear forms necessary and sufficient non-negative null set obtain Pólya positive and finite proof of Theorem prove Theorem proves the theorem quadratic form r+s+t=0 rearrangement replaced result Riesz satisfied Stieltjes integral strictly monotonic strictly positive sufficient condition suffixes summation Suppose Theorem 13 Theorem 9 theorem concerning theory true unless upper bound values W. H. Young write x₁ zero α₁ ακ Σα ΣΣ
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