Banachâ Hilbert Spaces Vector Measures And Group Representations

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Banach-Hilbert Spaces, Vector Measures and Group Representations

Tsoy-Wo Ma
Banach Hilbert Spaces Vector Measures and Group Representations Book PDF

Author : Tsoy-Wo Ma
Publisher : World Scientific
Page : 606 pages
File Size : 44,5 Mb
Release : 2002-01-01
Category : Mathematics
ISBN : 9812380388

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Banach-Hilbert Spaces, Vector Measures and Group Representations by Tsoy-Wo Ma Pdf

This book provides an elementary introduction to classical analysis on normed spaces, with special attention paid to fixed points, calculus, and ordinary differential equations. It contains a full treatment of vector measures on delta rings without assuming any scalar measure theory and hence should fit well into existing courses. The relation between group representations and almost periodic functions is presented. The mean values offer an infinite-dimensional analogue of measure theory on finite-dimensional Euclidean spaces. This book is ideal for beginners who want to get through the basic material as soon as possible and then do their own research immediately.

Banach–Hilbert Spaces, Vector Measures and Group Representations

Tsoy–Wo Ma
Banach Hilbert Spaces Vector Measures and Group Representations Book PDF

Author : Tsoy–Wo Ma
Publisher : World Scientific Publishing Company
Page : 620 pages
File Size : 45,6 Mb
Release : 2002-06-13
Category : Mathematics
ISBN : 9789813105980

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Banach–Hilbert Spaces, Vector Measures and Group Representations by Tsoy–Wo Ma Pdf

This book provides an elementary introduction to classical analysis on normed spaces, with special attention paid to fixed points, calculus, and ordinary differential equations. It contains a full treatment of vector measures on delta rings without assuming any scalar measure theory and hence should fit well into existing courses. The relation between group representations and almost periodic functions is presented. The mean values offer an infinitedimensional analogue of measure theory on finitedimensional Euclidean spaces. This book is ideal for beginners who want to get through the basic material as soon as possible and then do their own research immediately.

Infinite-dimensional Representations of 2-groups

John C. Baez
Infinite dimensional Representations of 2 groups Book PDF

Author : John C. Baez
Publisher : American Mathematical Soc.
Page : 120 pages
File Size : 44,8 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821872840

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Infinite-dimensional Representations of 2-groups by John C. Baez Pdf

A “$2$-group'' is a category equipped with a multiplication satisfying laws like those of a group. Just as groups have representations on vector spaces, $2$-groups have representations on “$2$-vector spaces'', which are categories analogous to vector spaces. Unfortunately, Lie $2$-groups typically have few representations on the finite-dimensional $2$-vector spaces introduced by Kapranov and Voevodsky. For this reason, Crane, Sheppeard and Yetter introduced certain infinite-dimensional $2$-vector spaces called ``measurable categories'' (since they are closely related to measurable fields of Hilbert spaces), and used these to study infinite-dimensional representations of certain Lie $2$-groups. Here they continue this work.

They begin with a detailed study of measurable categories. Then they give a geometrical description of the measurable representations, intertwiners and $2$-intertwiners for any skeletal measurable $2$-group. They study tensor products and direct sums for representations, and various concepts of subrepresentation. They describe direct sums of intertwiners, and sub-intertwiners--features not seen in ordinary group representation theory and study irreducible and indecomposable representations and intertwiners. They also study “irretractable'' representations--another feature not seen in ordinary group representation theory. Finally, they argue that measurable categories equipped with some extra structure deserve to be considered “separable $2$-Hilbert spaces'', and compare this idea to a tentative definition of $2$-Hilbert spaces as representation categories of commutative von Neumann algebras.

Theory of Group Representations and Applications

Asim Orhan Barut,Ryszard R?czka
Theory of Group Representations and Applications Book PDF

Author : Asim Orhan Barut,Ryszard R?czka
Publisher : World Scientific
Page : 750 pages
File Size : 47,6 Mb
Release : 1986
Category : Mathematics
ISBN : 9971502178

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Theory of Group Representations and Applications by Asim Orhan Barut,Ryszard R?czka Pdf

Lie!algebras - Topological!groups - Lie!groups - Representations - Special!functions - Induced!representations.

Representations of Finite and Compact Groups

Barry Simon
Representations of Finite and Compact Groups Book PDF

Author : Barry Simon
Publisher : American Mathematical Soc.
Page : 288 pages
File Size : 51,5 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 082187196X

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Representations of Finite and Compact Groups by Barry Simon Pdf

This book is a comprehensive pedagogical presentation of the theory of representation of finite and compact Lie groups that would be of interest to research mathematicians and graduate students interested in group theory and generalizations, topological groups, and Lie groups. Representation theory is discussed on finite groups of rotations, permutation groups, and classical compact Lie groups. The Weyl character formula is proved.