Sökning: "Integral transforms"
Visar resultat 1 - 5 av 12 avhandlingar innehållade orden Integral transforms.
1. Inverse Problems in Tomography and Fast Methods for Singular Convolutions
Sammanfattning : There are two, partially interlaced, themes treated in this thesis; inverse problems of tomographic type and fast and accurate methods for the application of convolution operators. Regarding the first theme, the inverse problem of Doppler tomography is considered and the Doppler moment transform is introduced for that purpose. LÄS MER
2. On the modelling of ultrasonic testing using boundary integral equation methods
Sammanfattning : Ultrasonic nondestructive testing has important applications in, for example, the nuclearpower and aerospace industries, where it is used to inspect safety-critical parts for flaws.For safe and reliable testing, mathematical models of the ultrasonic measurement systemsare invaluable tools. LÄS MER
3. Application of fast backprojection techniques for some inverse problems of integral geometry
Sammanfattning : In this thesis we study some mathematical inverse problems concerning the determination of a function from circular averages, which appear in certain radar applications, and the determination of a function from its line integrals, which appear in the well known problem of computerized tomographic imaging (CT). The thesis is divided into three parts. LÄS MER
4. Studies of vector tomography
Sammanfattning : The motivation to study the kind of problems appearing in this thesis has been ultrasound measurements of flows, from which velocity spectra along lines can be determined. These velocity spectra can mathematically be described by a new non-linear transform, here called the Doppler Spectral Transform (DST). LÄS MER
5. Amoebas, Discriminants, and Hypergeometric Functions
Sammanfattning : This thesis consists of six chapters. In Chapter 1 we give some historical background to the topic of the thesis together with the fundamental definitions and results that the thesis is based on. In Chapter 2 we study Mellin transforms of rational functions and investigate their analytic continuations. LÄS MER