Leon Ehrenpreis
- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198509783
- eISBN:
- 9780191709166
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198509783.001.0001
- Subject:
- Mathematics, Mathematical Physics
Radon showed how to write arbitrary functions in Rn in terms of the characteristic functions (delta functions) of hyperplanes. This idea leads to various generalizations. For example, R can be ...
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Radon showed how to write arbitrary functions in Rn in terms of the characteristic functions (delta functions) of hyperplanes. This idea leads to various generalizations. For example, R can be replaced by a more general group and “plane” can be replaced by other types of geometric objects. All this is for the “nonparametric” Radon transform. For the parametric Radon transform, this book parametrizes the points of the geometric objects, leading to differential equations in the parameters because the Radon transform is overdetermined. Such equations were first studied by F. John. This book elaborates on them and puts them in a general framework.Less
Radon showed how to write arbitrary functions in Rn in terms of the characteristic functions (delta functions) of hyperplanes. This idea leads to various generalizations. For example, R can be replaced by a more general group and “plane” can be replaced by other types of geometric objects. All this is for the “nonparametric” Radon transform. For the parametric Radon transform, this book parametrizes the points of the geometric objects, leading to differential equations in the parameters because the Radon transform is overdetermined. Such equations were first studied by F. John. This book elaborates on them and puts them in a general framework.
A. A. Ivanov
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198527596
- eISBN:
- 9780191713163
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198527596.003.0003
- Subject:
- Mathematics, Pure Mathematics
This section modifies the classical amalgam H to obtain the amalgam G which eventually leads to J4. The core of the modification is a triple isomorphism which explains the non-vanishing cohomology of ...
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This section modifies the classical amalgam H to obtain the amalgam G which eventually leads to J4. The core of the modification is a triple isomorphism which explains the non-vanishing cohomology of the natural 6-dimensional orthogonal module of the triform group. Although the modifications looks like an innocent move, almost immediately exceptional structures like Mathieu groups appear.Less
This section modifies the classical amalgam H to obtain the amalgam G which eventually leads to J4. The core of the modification is a triple isomorphism which explains the non-vanishing cohomology of the natural 6-dimensional orthogonal module of the triform group. Although the modifications looks like an innocent move, almost immediately exceptional structures like Mathieu groups appear.
Leon Ehrenpreis
- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198509783
- eISBN:
- 9780191709166
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198509783.003.0001
- Subject:
- Mathematics, Mathematical Physics
This introductory chapter presents a detailed summary of the highlights of the book. In particular, it explains in various contexts why the Radon transform leads to a “basis” for all functions, and ...
More
This introductory chapter presents a detailed summary of the highlights of the book. In particular, it explains in various contexts why the Radon transform leads to a “basis” for all functions, and the origins of John-like equations.Less
This introductory chapter presents a detailed summary of the highlights of the book. In particular, it explains in various contexts why the Radon transform leads to a “basis” for all functions, and the origins of John-like equations.
