Geometry Of Sets And Measures In Euclidean Spaces

Author : Pertti Mattila
Publisher : Cambridge University Press
ISBN 13 : 9780521655958
Total Pages : 360 pages
Book Rating : 4.51/5 ( download)

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Download or read book Geometry of Sets and Measures in Euclidean Spaces written by Pertti Mattila and published by Cambridge University Press. This book was released on 1999-02-25 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the geometric properties of general sets and measures in euclidean space.

Author : Pertti Mattila
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.43/5 ( download)

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Download or read book Geometry of sets and measures in euclidean spaces written by Pertti Mattila and published by . This book was released on 1992 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Frank Jones
Publisher : Jones & Bartlett Learning
ISBN 13 : 9780763717087
Total Pages : 626 pages
Book Rating : 4.88/5 ( download)

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Download or read book Lebesgue Integration on Euclidean Space written by Frank Jones and published by Jones & Bartlett Learning. This book was released on 2001 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: "'Lebesgue Integration on Euclidean Space' contains a concrete, intuitive, and patient derivation of Lebesgue measure and integration on Rn. It contains many exercises that are incorporated throughout the text, enabling the reader to apply immediately the new ideas that have been presented" --

Author : Jan Rataj
Publisher : Springer
ISBN 13 : 3030181839
Total Pages : 256 pages
Book Rating : 4.33/5 ( download)

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Download or read book Curvature Measures of Singular Sets written by Jan Rataj and published by Springer. This book was released on 2019-06-22 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book describes how curvature measures can be introduced for certain classes of sets with singularities in Euclidean spaces. Its focus lies on sets with positive reach and some extensions, which include the classical polyconvex sets and piecewise smooth submanifolds as special cases. The measures under consideration form a complete system of certain Euclidean invariants. Techniques of geometric measure theory, in particular, rectifiable currents are applied, and some important integral-geometric formulas are derived. Moreover, an approach to curvatures for a class of fractals is presented, which uses approximation by the rescaled curvature measures of small neighborhoods. The book collects results published during the last few decades in a nearly comprehensive way.

Author : Pertti Mattila
Publisher : Cambridge University Press
ISBN 13 : 1009288083
Total Pages : 181 pages
Book Rating : 4.88/5 ( download)

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Download or read book Rectifiability written by Pertti Mattila and published by Cambridge University Press. This book was released on 2023-01-12 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: A broad survey of the theory of rectifiability and its deep connections to numerous different areas of mathematics.

Author : Herbert Federer
Publisher : Springer
ISBN 13 : 3642620108
Total Pages : 694 pages
Book Rating : 4.02/5 ( download)

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Download or read book Geometric Measure Theory written by Herbert Federer and published by Springer. This book was released on 2014-11-25 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is a major treatise in mathematics and is essential in the working library of the modern analyst." (Bulletin of the London Mathematical Society)

Author : K. J. Falconer
Publisher : Cambridge University Press
ISBN 13 : 9780521337052
Total Pages : 184 pages
Book Rating : 4.54/5 ( download)

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Download or read book The Geometry of Fractal Sets written by K. J. Falconer and published by Cambridge University Press. This book was released on 1985 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematical study of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Considers questions of local density, the existence of tangents of such sets as well as the dimensional properties of their projections in various directions.

Author : Francesco Maggi
Publisher :
ISBN 13 : 9781107471726
Total Pages : 454 pages
Book Rating : 4.29/5 ( download)

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Download or read book Sets of Finite Perimeter and Geometric Variational Problems written by Francesco Maggi and published by . This book was released on 2012 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Steven G. Krantz
Publisher : Springer Science & Business Media
ISBN 13 : 1461215749
Total Pages : 311 pages
Book Rating : 4.45/5 ( download)

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Download or read book The Geometry of Domains in Space written by Steven G. Krantz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: The analysis of Euclidean space is well-developed. The classical Lie groups that act naturally on Euclidean space-the rotations, dilations, and trans lations-have both shaped and guided this development. In particular, the Fourier transform and the theory of translation invariant operators (convolution transforms) have played a central role in this analysis. Much modern work in analysis takes place on a domain in space. In this context the tools, perforce, must be different. No longer can we expect there to be symmetries. Correspondingly, there is no longer any natural way to apply the Fourier transform. Pseudodifferential operators and Fourier integral operators can playa role in solving some of the problems, but other problems require new, more geometric, ideas. At a more basic level, the analysis of a smoothly bounded domain in space requires a great deal of preliminary spadework. Tubular neighbor hoods, the second fundamental form, the notion of "positive reach", and the implicit function theorem are just some of the tools that need to be invoked regularly to set up this analysis. The normal and tangent bundles become part of the language of classical analysis when that analysis is done on a domain. Many of the ideas in partial differential equations-such as Egorov's canonical transformation theorem-become rather natural when viewed in geometric language. Many of the questions that are natural to an analyst-such as extension theorems for various classes of functions-are most naturally formulated using ideas from geometry.

Author : Pertti Mattila
Publisher : Cambridge University Press
ISBN 13 : 1107107350
Total Pages : 455 pages
Book Rating : 4.59/5 ( download)

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Download or read book Fourier Analysis and Hausdorff Dimension written by Pertti Mattila and published by Cambridge University Press. This book was released on 2015-07-22 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern text examining the interplay between measure theory and Fourier analysis.