The Resource Analysis of Spherical Symmetries in Euclidean Spaces, by Claus Müller, (electronic resource)

Analysis of Spherical Symmetries in Euclidean Spaces, by Claus Müller, (electronic resource)

Label
Analysis of Spherical Symmetries in Euclidean Spaces
Title
Analysis of Spherical Symmetries in Euclidean Spaces
Statement of responsibility
by Claus Müller
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
This book gives a new and direct approach into the theories of special functions with emphasis on spherical symmetry in Euclidean spaces of ar­ bitrary dimensions. Essential parts may even be called elementary because of the chosen techniques. The central topic is the presentation of spherical harmonics in a theory of invariants of the orthogonal group. H. Weyl was one of the first to point out that spherical harmonics must be more than a fortunate guess to simplify numerical computations in mathematical physics. His opinion arose from his occupation with quan­ tum mechanics and was supported by many physicists. These ideas are the leading theme throughout this treatise. When R. Richberg and I started this project we were surprised, how easy and elegant the general theory could be. One of the highlights of this book is the extension of the classical results of spherical harmonics into the complex. This is particularly important for the complexification of the Funk-Hecke formula, which is successfully used to introduce orthogonally invariant solutions of the reduced wave equation. The radial parts of these solutions are either Bessel or Hankel functions, which play an important role in the mathematical theory of acoustical and optical waves. These theories often require a detailed analysis of the asymptotic behavior of the solutions. The presented introduction of Bessel and Hankel functions yields directly the leading terms of the asymptotics. Approximations of higher order can be deduced
Member of
http://library.link/vocab/creatorName
Müller, Claus
Dewey number
515
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
ZvNnpScaHxY
Image bit depth
0
Language note
English
LC call number
QA299.6-433
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Applied Mathematical Sciences,
Series volume
129
http://library.link/vocab/subjectName
  • Global analysis (Mathematics)
  • Geometry
  • Chemistry
  • Analysis
  • Geometry
  • Math. Applications in Chemistry
  • Theoretical, Mathematical and Computational Physics
Label
Analysis of Spherical Symmetries in Euclidean Spaces, by Claus Müller, (electronic resource)
Instantiates
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
1 Notations and Basic Theorems> -- 1 The General Theory 9 -- §2 Primitive Spaces -- §3 The Completeness -- §4 The Funk-Hecke Formula -- §5 Representations and Interpolations -- §6 Homogeneous Harmonics -- 2 The Specific Theories -- §7 The Legendre Polynomials -- §8 The Laplace Integrals -- §9 The Gegenbauer Polynomials -- §10 The Associated Legendre Functions -- §1 The Associated Spaces yjn(q) -- §12 Harmonic Differential Operators -- §13 Maxwell’s Theory of Multipoles -- 3 Spherical Harmonics and Differential Equations -- §14 The Laplace-Beltrami Operators -- §15 Spherical Harmonics as Eigenfunctions -- §16 The Legendre Differential Equation -- §17 The Legendre Functions as Hypergeometric Functions -- 4 Analysis on the Complex Unit Spheres -- §18 Homogeneous Harmonics in ?q -- §19 Invariant Integrals on S*q-1 -- §20 Complexification of the Funk-Hecke Formula -- §21 An Alternative System of Legendre Functions -- 5 The Bessel Functions -- §22 Regular Bessel Functions -- §23 Regular Hankel Functions -- §24 Recursive and Asymptotic Relations -- §25 Addition Formulas for Hankel Functions of Order Zero -- §26 Exponential Integrals with Bessel Functions -- §27 The Traditional Notations -- 6 Integral Transforms -- §28 Fourier Integrals -- §29 The Fourier Representation Theorem -- §30 The Parseval Identity -- §31 Examples -- 7 The Radon Transform -- §32 Radon Transforms and Fourier Transforms -- §33 Radon Transforms and Spherical Symmetries -- §34 The Nicholson Formulas -- 8 Appendix -- §35 The ?-Function. -- §36 The Hypergeometric Function -- §37 Elementary Asymptotics -- References
Dimensions
unknown
Edition
1st ed. 1998.
Extent
1 online resource (VIII, 226 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461205814
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-1-4612-0581-4
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000089188
  • (SSID)ssj0001295834
  • (PQKBManifestationID)11711502
  • (PQKBTitleCode)TC0001295834
  • (PQKBWorkID)11347131
  • (PQKB)10367223
  • (DE-He213)978-1-4612-0581-4
  • (MiAaPQ)EBC3075121
  • (EXLCZ)993400000000089188
Label
Analysis of Spherical Symmetries in Euclidean Spaces, by Claus Müller, (electronic resource)
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
1 Notations and Basic Theorems> -- 1 The General Theory 9 -- §2 Primitive Spaces -- §3 The Completeness -- §4 The Funk-Hecke Formula -- §5 Representations and Interpolations -- §6 Homogeneous Harmonics -- 2 The Specific Theories -- §7 The Legendre Polynomials -- §8 The Laplace Integrals -- §9 The Gegenbauer Polynomials -- §10 The Associated Legendre Functions -- §1 The Associated Spaces yjn(q) -- §12 Harmonic Differential Operators -- §13 Maxwell’s Theory of Multipoles -- 3 Spherical Harmonics and Differential Equations -- §14 The Laplace-Beltrami Operators -- §15 Spherical Harmonics as Eigenfunctions -- §16 The Legendre Differential Equation -- §17 The Legendre Functions as Hypergeometric Functions -- 4 Analysis on the Complex Unit Spheres -- §18 Homogeneous Harmonics in ?q -- §19 Invariant Integrals on S*q-1 -- §20 Complexification of the Funk-Hecke Formula -- §21 An Alternative System of Legendre Functions -- 5 The Bessel Functions -- §22 Regular Bessel Functions -- §23 Regular Hankel Functions -- §24 Recursive and Asymptotic Relations -- §25 Addition Formulas for Hankel Functions of Order Zero -- §26 Exponential Integrals with Bessel Functions -- §27 The Traditional Notations -- 6 Integral Transforms -- §28 Fourier Integrals -- §29 The Fourier Representation Theorem -- §30 The Parseval Identity -- §31 Examples -- 7 The Radon Transform -- §32 Radon Transforms and Fourier Transforms -- §33 Radon Transforms and Spherical Symmetries -- §34 The Nicholson Formulas -- 8 Appendix -- §35 The ?-Function. -- §36 The Hypergeometric Function -- §37 Elementary Asymptotics -- References
Dimensions
unknown
Edition
1st ed. 1998.
Extent
1 online resource (VIII, 226 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461205814
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-1-4612-0581-4
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000089188
  • (SSID)ssj0001295834
  • (PQKBManifestationID)11711502
  • (PQKBTitleCode)TC0001295834
  • (PQKBWorkID)11347131
  • (PQKB)10367223
  • (DE-He213)978-1-4612-0581-4
  • (MiAaPQ)EBC3075121
  • (EXLCZ)993400000000089188

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