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AuthorMaurin, Krzysztof. author
TitleAnalysis [electronic resource] : Part II Integration, Distributions, Holomorphic Functions, Tensor and Harmonic Analysis / by Krzysztof Maurin
ImprintDordrecht : Springer Netherlands, 1980
Connect tohttp://dx.doi.org/10.1007/978-94-009-8939-9
Descript XXXIV, 829 p. online resource

SUMMARY

The extraordinarily rapid advances made in mathematics since World War II have resulted in analysis becoming an enormous organism spreadยญ ing in all directions. Gone for good surely are the days of the great French "courses of analysis" which embodied the whole of the "anaยญ lytical" knowledge of the times in three volumes-as the classical work of Camille Jordan. Perhaps that is why present-day textbooks of analยญ ysis are disproportionately modest relative to the present state of the art. More: they have "retreated" to the state before Jordan and Goursat. In recent years the scene has been changing rapidly: Jean Dieudonยญ ne is offering us his monumentel Elements d'Analyse (10 volumes) written in the spirit of the great French Course d'Analyse. To the best of my knowledge, the present book is the only one of its size: starting from scratch-from rational numbers, to be precise-it goes on to the theory of distributions, direct integrals, analysis on comยญ plex manifolds, Kahler manifolds, the theory of sheaves and vector bunยญ dles, etc. My objective has been to show the young reader the beauty and wealth of the unsual world of modern mathematical analysis and to show that it has its roots in the great mathematics of the 19th century and mathematical physics. I do know that the young mind eagerly drinks in beautiful and difficult things, rejoicing in the fact that the world is great and teeming with adventure


CONTENT

XII. Topology. Uniform Structures. Function Spaces -- XIII. Theory of the Integral -- XIV. Tensor Analysis. Harmonic Forms. Cohomology. Applications to Electrodynamics -- XV. Elementary Properties of Holomorphic Functions of Several Variables. Harmonic Functions -- XVI. Complex Analysis in One Dimension (Riemann Surfaces -- XVII. Normal and Paracompact Spaces. Partition of Unity. -- XVIII. Measurable Mappings. The Transport of a Measure. Convolutions of Measures and Functions -- XIX. The Theory of Distributions. Harmonic Analysis -- Index of Symbols -- Name Index


Mathematics Mathematical analysis Analysis (Mathematics) Mathematics Analysis



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