One hundred years ago (1904) Hermann Minkowski [58] posed a problem: to re� 2 construct an even function I on the sphere 8 from knowledge of the integrals MI (C) = fc Ids over big circles C. Paul Funk found an explicit reconstruction formula for I from data of big circle integrals. Johann Radon studied a similar problem for the Eu� clidean plane and space. The interest in reconstruction problems like Minkowski� Funk's and Radon's has grown tremendously in the last four decades, stimulated by the spectrum of new modalities of image reconstruction. These are X-ray, MRI, gamma and positron radiography, ultrasound, seismic tomography, electron mi� croscopy, synthetic radar imaging and others. The physical principles of these methods are very different, however their mathematical models and solution meth� ods have very much in common. The umbrella name reconstructive integral geom� etryl is used to specify the variety of these problems and methods. The objective of this book is to present in a uniform way the scope of well� known and recent results and methods in the reconstructive integral geometry. We do not touch here the problems arising in adaptation of analytic methods to numerical reconstruction algorithms. We refer to the books [61], [62] which are focused on these problems. Various aspects of interplay of integral geometry and differential equations are discussed in Chapters 7 and 8. The results presented here are partially new.

Cr�ticas

"This book is an excellent overview of the field of integral geometry with emphasis on the functional analytic and differential geometric aspects. The author proves theorems for some of the most important Radon transforms, including transforms on hyperplanes, k-planes, lines, and spheres, and he investigates incomplete (limited) data problems including microlocal analytic issues...This book contains many treasures in integral geometry...and it belongs on the shelf of any analyst or geometer who would like to see how deep functional analysis and differential geometry are used to solve important problems in integral geometry." ―Mathematical Reviews

��ber diesen Titel� kann sich auf eine andere Ausgabe dieses Titels beziehen.

Anbieterinformationen

Quality books, speedy shipping, and great customer service! Please note that used items may not include access codes or cards, CD's or other accessories, regardless of what is stated in item title. If you need to guarantee that these items are included, please purchase a brand new copy.

Zur Homepage des Verk�ufers

Unternehmensdaten des Verk�ufers

J2B Holdings, LLC
13770 NOEL RD, #803600, Dallas, TX, 75240, U.S.A.

Gesch�ftsbedingungen und Versandinformationen

Verkaufsbedingungen

We guarantee the condition of every book as it's described on the AbeBooks web
sites. Please note that used items may not include access codes or cards, CD's
or other accessories, regardless of what is stated in item title. If you need to
guarantee that these items are included, please purchase a brand new copy.

All requests for refunds and/or returns will be processed in accordance with
AbeBooks policies. If you're dissatisfied with your purchase (Incorrect Book/Not
as Described/Damaged) or if ...

Mehr Information

Versandbedingungen

Books ordered via expedited shipping should arrive between 2 and 7 business days after shipment confirmation. Books ordered via standard shipping should arrive between 4 and 14 business days after shipment confirmation.