[PDF] Reconstructive Integral Geometry [electronic resource] - eBookmela

Reconstructive Integral Geometry [electronic resource]

New Added
Reconstructive Integral Geometry [electronic resource]
Likes+254
Telegram icon Share on Telegram

Reconstructive Integral Geometry [electronic resource]

User Rating: Be the first one!

Author: Palamodov, V. P. (Viktor Pavlovich)

Added by: sketch

Added Date: 2015-12-29

Language: eng

Subjects: Mathematics, Fourier analysis, Integral transforms, Fourier analysis, Integral transforms, Mathematics

Publishers: Basel : Birkhäuser Basel : Imprint : Birkhäuser

Collections: folkscanomy miscellaneous, folkscanomy, additional collections

ISBN Number: 9783034879415, 3034879415

Pages Count: 600

PPI Count: 600

PDF Count: 1

Total Size: 225.46 MB

PDF Size: 14.31 MB

Extensions: djvu, epub, gif, pdf, gz, zip, torrent, log, mrc

Archive Url

Downloads: 2K

Views: 52

Total Files: 20

Media Type: texts

PDF With Zip
Reconstructive Integral Geometry [electronic resource]

April 4, 2022

Download PDF

14.31 MB 1PDF Files

Zip Big Size
Reconstructive Integral Geometry [electronic resource]

April 4, 2022

Download Zip

225.46 MB 20Files

Total Files: 7

PDF
Reconstructive Integral Geometry [electronic resource]
10 1007 978 3 0348 7941 5 pdf

Last Modified: 2015-12-29 04:56:45

Download

Size: 14.31 MB

EPUB
Reconstructive Integral Geometry [electronic resource]
10 1007 978 3 0348 7941 5 epub

Last Modified: 2024-02-10 10:03:04

Download

Size: 169.10 MB

GZ
Reconstructive Integral Geometry [electronic resource]
10 1007 978 3 0348 7941 5 abbyy gz

Last Modified: 2015-12-29 05:38:52

Download

Size: 4.88 MB

ZIP
Reconstructive Integral Geometry [electronic resource]
10 1007 978 3 0348 7941 5 daisy zip

Last Modified: 2024-02-10 09:59:20

Download

Size: 218.12 KB

TXT
Reconstructive Integral Geometry [electronic resource]
10 1007 978 3 0348 7941 5 djvu txt

Last Modified: 2016-01-06 11:49:25

Download

Size: 145.90 KB

ZIP
Reconstructive Integral Geometry [electronic resource]
10 1007 978 3 0348 7941 5 jp2 zip

Last Modified: 2015-12-29 05:04:02

Download

Size: 29.70 MB

TORRENT
Reconstructive Integral Geometry [electronic resource]
springer 10 1007 978 3 0348 7941 5 archi...torrent

Last Modified: 2024-02-10 10:03:08

Download

Size: 13.39 KB

Description

Reconstructive Integral Geometry
Author: Victor Palamodov
Published by Birkhäuser Basel
ISBN: 978-3-0348-9629-0
DOI: 10.1007/978-3-0348-7941-5

Table of Contents:

  • Distributions and Fourier Transform
  • Radon Transform
  • The Funk Transform
  • Reconstruction from Line Integrals
  • Flat Integral Transform
  • Incomplete Data Problems
  • Spherical Transform and Inversion
  • Algebraic Integral Transform
  • Notes

This book covers facts and methods for the reconstruction of a function in a real affine or projective space from data of integrals, particularly over lines, planes, and spheres. Recent results are collected stressing explicit analytic methods. Another focus consists of the relations between algebraic integral geometry and partial differential equations. A concise basic course in harmonic analysis and distribution theory is given in the first chapter. The first half of the book includes the ray, the spherical mean transforms in the plane or in 3-space, and inversion from incomplete data. It will be of particular interest to application oriented readers. Further chapters are devoted to the Funk-Radon transform on algebraic varieties of arbitrary dimension. The material appeals to graduates and researchers in pure and applied mathematics who are interested in image reconstruction, inverse problems or functional analysis
1 Distributions and Fourier Transform -- 1.1 Introduction -- 1.2 Distributions and generalized functions -- 1.3 Tempered distributions -- 1.4 Homogeneous distributions -- 1.5 Manifolds and differential forms -- 1.6 Push down and pull back -- 1.7 More on the Fourier transform -- 1.8 Bandlimited functions and interpolation -- 2 Radon Transform -- 2.1 Properties -- 2.2 Inversion formulae -- 2.3 Alternative formulae -- 2.4 Range conditions -- 2.5 Frequency analysis -- 2.6 Radon transform of differential forms -- 3 The Funk Transform -- 3.1 Factorable mappings -- 3.2 Spaces of constant curvature -- 3.3 Inversion of the Funk transform -- 3.4 Radon's inversion via Funk's inversion -- 3.5 Unified form -- 3.6 Funk-Radon transform and wave fronts -- 3.7 Integral transform of boundary discontinuities -- 3.8 Nonlinear artifacts -- 3.9 Pizetti formula for arbitrary signature -- 4 Reconstruction from Line Integrals -- 4.1 Pencils of lines and John's equation -- 4.2 Sources at infinity -- 4.3 Reduction to the Radon transform -- 4.4 Rays tangent to a surface -- 4.5 Sources on a proper curve -- 4.6 Reconstruction from plane integrals of sources -- 4.7 Line integrals of differential forms -- 4.8 Exponential ray transform -- 4.9 Attenuated ray transform -- 4.10 Inversion formulae -- 4.11 Range conditions -- 5 Flat Integral Transform -- 5.1 Reconstruction problem -- 5.2 Odd-dimensional subspaces -- 5.3 Even dimension -- 5.4 Range of the flat transform -- 5.5 Duality for the Funk transform -- 5.6 Duality in Euclidean space -- 6 Incomplete Data Problems -- 6.1 Completeness condition -- 6.2 Radon transform of Gabor functions -- 6.3 Reconstruction from limited angle data -- 6.4 Exterior problem -- 6.5 The parametrix method -- 7 Spherical Transform and Inversion -- 7.1 Problems -- 7.2 Arc integrals in the plane -- 7.3 Hemispherical integrals in space -- 7.4 Incomplete data -- 7.5 Spheres centred on a sphere -- 7.6 Spheres tangent to a manifold -- 7.7 Characteristic Cauchy problem -- 7.8 Fundamental solution for the adjoint operator -- 8 Algebraic Integral Transform -- 8.1 Problems -- 8.2 Special cases -- 8.3 Multiplicative differential equations -- 8.4 Funk transform of Leray forms -- 8.5 Differential equations for hypersurface integrals -- 8.6 Howard's equations -- 8.7 Range of differential operators -- 8.8 Decreasing solutions of Maxwell's system -- 8.9 Symmetric differential forms -- 9 Notes -- Notes to Chapter 1 -- Notes to Chapter 2 -- Notes to Chapter 3 -- Notes to Chapter 4 -- Notes to Chapter 5 -- Notes to Chapter 6 -- Notes to Chapter 7 -- Notes to Chapter 8

You May Also Like

We will be happy to hear your thoughts

Leave a reply

eBookmela
Logo
Register New Account