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Geometry and Analysis of Metric Spaces Via Weighted Partitions, Kigami Jun


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Автор: Kigami Jun
Название:  Geometry and Analysis of Metric Spaces Via Weighted Partitions
ISBN: 9783030541538
Издательство: Springer
Классификация:




ISBN-10: 3030541533
Обложка/Формат: Paperback
Страницы: 164
Вес: 0.25 кг.
Дата издания: 02.01.2021
Язык: English
Размер: 23.39 x 15.60 x 0.94 cm
Ссылка на Издательство: Link
Поставляется из: Германии
Описание:

The aim of these lecture notes is to propose a systematic framework for geometry and analysis on metric spaces. The central notion is a partition (an iterated decomposition) of a compact metric space. Via a partition, a compact metric space is associated with an infinite graph whose boundary is the original space. Metrics and measures on the space are then studied from an integrated point of view as weights of the partition. In the course of the text:

  1. It is shown that a weight corresponds to a metric if and only if the associated weighted graph is Gromov hyperbolic.
  2. Various relations between metrics and measures such as bilipschitz equivalence, quasisymmetry, Ahlfors regularity, and the volume doubling property are translated to relations between weights. In particular, it is shown that the volume doubling property between a metric and a measure corresponds to a quasisymmetry between two metrics in the language of weights.
  3. The Ahlfors regular conformal dimension of a compact metric space is characterized as the critical index of p-energies associated with the partition and the weight function corresponding to the metric.

These notes should interest researchers and PhD students working in conformal geometry, analysis on metric spaces, and related areas.





Nested Partitions Method, Theory and Applications

Автор: Leyuan Shi; Sigurdur ?lafsson
Название: Nested Partitions Method, Theory and Applications
ISBN: 1441944206 ISBN-13(EAN): 9781441944207
Издательство: Springer
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Цена: 14673.00 р.
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Описание: There is an ever-increasing need to solve optimization problems in a wide variety of science and engineering applications. This up-to-date and highly relevant book provides a cutting-edge research tool to use for large-scale, complex systems optimization.

Sobolev Spaces on Metric Measure Spaces

Автор: Heinonen
Название: Sobolev Spaces on Metric Measure Spaces
ISBN: 1107092345 ISBN-13(EAN): 9781107092341
Издательство: Cambridge Academ
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Цена: 19800.00 р.
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Описание: Analysis on metric spaces is a field that has expanded dramatically since the 1990s. Written by some of the founders of the theory, this book provides a coherent treatment from first principles. It is an ideal introduction for graduate students and a useful reference for experts in the field.

Normal Partitions and Hierarchical Fillings of N-Dimensional Spaces

Автор: Zhizhin Gennadiy Vladimirovich
Название: Normal Partitions and Hierarchical Fillings of N-Dimensional Spaces
ISBN: 1799867692 ISBN-13(EAN): 9781799867692
Издательство: Mare Nostrum (Eurospan)
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Цена: 20236.00 р.
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Описание: Considers the construction of spaces of various dimensions from two to any finite dimension n, taking into account the indicated conditions, including zooming in on shapes, properties of geometric figures of higher dimensions, which have no analogue in three-dimensional space.

Irregularities of Partitions

Автор: Gabor Halasz; Vera T. Sos
Название: Irregularities of Partitions
ISBN: 3540505822 ISBN-13(EAN): 9783540505822
Издательство: Springer
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Цена: 16070.00 р.
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q-Series and Partitions

Автор: Dennis Stanton
Название: q-Series and Partitions
ISBN: 1468406396 ISBN-13(EAN): 9781468406399
Издательство: Springer
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Цена: 13974.00 р.
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Описание: This IMA Volume in Mathematics and its Applications q-Series and Partitions is based on the proceedings of a workshop which was an integral part of the 1987-88 IMA program on APPLIED COMBINATORICS.

Weighted Inequalities Of Hardy Type (Second Edition)

Автор: Persson Lars-Erik Et Al
Название: Weighted Inequalities Of Hardy Type (Second Edition)
ISBN: 981314064X ISBN-13(EAN): 9789813140646
Издательство: World Scientific Publishing
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Цена: 16790.00 р.
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Описание: Inequalities play an important role in almost all branches of mathematics as well as in other areas of science and engineering. This book surveys the present state of the theory of weighted integral inequalities of Hardy type, including modifications concerning Hardy-Steklov operators, and some basic results about Hardy-type inequalities and their limit (Carleman-Knopp type) inequalities. It also describes some rather new areas such as higher order and fractional order Hardy-type inequalities and integral inequalities on the cone of monotone functions, together with some applications and open problems.In this second edition, all chapters in the first edition have been updated with new information. Moreover, a new chapter contains new and complementary information concerning: (a) a convexity approach to prove and explain Hardy-type inequalities; (b) sharp constants; (c) scales of inequalities to characterize Hardy-type inequalities; (d) Hardy-type inequalities in other function spaces; and (e) a number of new open questions.

Normal Partitions and Hierarchical Fillings of N-Dimensional Spaces

Автор: Gennadiy Vladimirovich Zhizhin
Название: Normal Partitions and Hierarchical Fillings of N-Dimensional Spaces
ISBN: 1799867684 ISBN-13(EAN): 9781799867685
Издательство: Mare Nostrum (Eurospan)
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Цена: 26195.00 р.
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Описание: Considers the construction of spaces of various dimensions from two to any finite dimension n, taking into account the indicated conditions, including zooming in on shapes, properties of geometric figures of higher dimensions, which have no analogue in three-dimensional space.

Transfer Operators, Endomorphisms, and Measurable Partitions

Автор: Bezuglyi
Название: Transfer Operators, Endomorphisms, and Measurable Partitions
ISBN: 3319924168 ISBN-13(EAN): 9783319924168
Издательство: Springer
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Цена: 5589.00 р.
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Описание: The subject of this book stands at the crossroads of ergodic theory and measurable dynamics. With an emphasis on irreversible systems, the text presents a framework of multi-resolutions tailored for the study of endomorphisms, beginning with a systematic look at the latter. This entails a whole new set of tools, often quite different from those used for the “easier” and well-documented case of automorphisms. Among them is the construction of a family of positive operators (transfer operators), arising naturally as a dual picture to that of endomorphisms. The setting (close to one initiated by S. Karlin in the context of stochastic processes) is motivated by a number of recent applications, including wavelets, multi-resolution analyses, dissipative dynamical systems, and quantum theory. The automorphism-endomorphism relationship has parallels in operator theory, where the distinction is between unitary operators in Hilbert space and more general classes of operators such as contractions. There is also a non-commutative version: While the study of automorphisms of von Neumann algebras dates back to von Neumann, the systematic study of their endomorphisms is more recent; together with the results in the main text, the book includes a review of recent related research papers, some by the co-authors and their collaborators.

Machine scheduling to minimize weighted completion times.

Автор: Nicolо Gusmeroli
Название: Machine scheduling to minimize weighted completion times.
ISBN: 3319775278 ISBN-13(EAN): 9783319775272
Издательство: Springer
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Цена: 6986.00 р.
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Описание: This work reviews the most important results regarding the use of the ГЋВ±-point in Scheduling Theory. Lastly, the book explores the latest techniques used for many scheduling problems with different constraints, such as release dates, precedences, and parallel machines.

Metric in Measure Spaces

Автор: Yeh James J.
Название: Metric in Measure Spaces
ISBN: 9813200405 ISBN-13(EAN): 9789813200401
Издательство: World Scientific Publishing
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Цена: 8712.00 р.
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Описание:

Measure and metric are two fundamental concepts in measuring the size of a mathematical object. Yet there has been no systematic investigation of this relation. The book closes this gap.


Contents: Measure and Outer Measure; Construction of Outer Measures; Borel Measures; Hausdorff Measures; Covering Theorems; Differentiation of Measures; Averaging Operators and Differentiation of Integrals; Lebesgue Differentiation Theorem for Integrals; Hardy-Littlewood Maximal Functions; Density of Sets; Approximate Limit and Approximate Continuity; Lipschitz Mappings;

Readership: Mathematicians and graduate students in mathematics.

Unbounded weighted composition operators in l(2)-spaces

Автор: Budzynski, Piotr Jablonski, Zenon Jung, Il Bong Stochel, Jan
Название: Unbounded weighted composition operators in l(2)-spaces
ISBN: 3319740385 ISBN-13(EAN): 9783319740386
Издательство: Springer
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Цена: 6288.00 р.
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Описание:

This book establishes the foundations of the theory of bounded and unbounded weighted composition operators in L -spaces. It develops the theory in full generality, meaning that the corresponding composition operators are not assumed to be well defined. A variety of seminormality properties of unbounded weighted composition operators are characterized.

The first-ever criteria for subnormality of unbounded weighted composition operators are provided and the subtle interplay between the classical moment problem, graph theory and the injectivity problem for weighted composition operators is revealed. The relationships between weighted composition operators and the corresponding multiplication and composition operators are investigated. The optimality of the obtained results is illustrated by a variety of examples, including those of discrete and continuous types.

The book is primarily aimed at researchers in single or multivariable operator theory.

Metric in measure spaces

Автор: Yeh, James J.
Название: Metric in measure spaces
ISBN: 9813200391 ISBN-13(EAN): 9789813200395
Издательство: World Scientific Publishing
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Цена: 14256.00 р.
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Описание:

Measure and metric are two fundamental concepts in measuring the size of a mathematical object. Yet there has been no systematic investigation of this relation. The book closes this gap.


Contents: Measure and Outer Measure; Construction of Outer Measures; Borel Measures; Hausdorff Measures; Covering Theorems; Differentiation of Measures; Averaging Operators and Differentiation of Integrals; Lebesgue Differentiation Theorem for Integrals; Hardy-Littlewood Maximal Functions; Density of Sets; Approximate Limit and Approximate Continuity; Lipschitz Mappings;

Readership: Mathematicians and graduate students in mathematics.


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