The thesis summarizes publications that contain the author’s contribution to the field of
multivariate Fourier transforms and their applications within mathematical physics. The
corresponding research was conducted following the award of the doctoral degree (Ph.D.).
The Fourier–Weyl transforms comprise discrete transforms constructed on finite fragments
of the Weyl group invariant lattices. Ten types of Weyl orbit functions, restricted to the
fundamental domain of the affine Weyl groups and their even subgroups, induce the forward
and backward discrete transforms. The related 2D and 3D interpolation problems and
cubature formulas are developed. The transforms are linked to the Kac–Walton formulas
and Kac–Peterson matrices in conformal field theory and applied to vibration models in
solid state physics. The entire author’s published body of work in this field comprises
16 articles in impacted journals and several conference proceedings. The presented nine
articles, published in impacted journals, are chosen to represent the entire collection of
the author’s publications in the field and contain key notions and original concepts of the
author’s contribution.
cze
dc.language.iso
en
en
dc.publisher
ČVUT. Fakulta jaderná a fyzikálně inženýrská.
cze
dc.title
MULTIVARIATE FOURIER–WEYL TRANSFORMS AND THEIR APPLICATIONS
