Connecting (Anti)Symmetric Trigonometric Transforms to Dual-Root Lattice Fourier–Weyl Transforms
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F21%3A00345104" target="_blank" >RIV/68407700:21340/21:00345104 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.3390/sym13010061" target="_blank" >https://doi.org/10.3390/sym13010061</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/sym13010061" target="_blank" >10.3390/sym13010061</a>
Alternative languages
Result language
angličtina
Original language name
Connecting (Anti)Symmetric Trigonometric Transforms to Dual-Root Lattice Fourier–Weyl Transforms
Original language description
Explicit links of the multivariate discrete (anti)symmetric cosine and sine transforms with the generalized dual-root lattice Fourier–Weyl transforms are constructed. Exact identities between the (anti)symmetric trigonometric functions and Weyl orbit functions of the crystallographic root systems and are utilized to connect the kernels of the discrete transforms. The point and label sets of the 32 discrete (anti)symmetric trigonometric transforms are expressed as fragments of the rescaled dual root and weight lattices inside the closures of Weyl alcoves. A case-by-case analysis of the inherent extended Coxeter–Dynkin diagrams specifically relates the weight and normalization functions of the discrete transforms. The resulting unique coupling of the transforms is achieved by detailing a common form of the associated unitary transform matrices. The direct evaluation of the corresponding unitary transform matrices is exemplified for several cases of the bivariate transforms.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10300 - Physical sciences
Result continuities
Project
<a href="/en/project/GA19-19535S" target="_blank" >GA19-19535S: Fourier methods of special functions of affine Weyl groups</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Symmetry
ISSN
2073-8994
e-ISSN
2073-8994
Volume of the periodical
13
Issue of the periodical within the volume
1
Country of publishing house
CH - SWITZERLAND
Number of pages
28
Pages from-to
—
UT code for WoS article
000610742800001
EID of the result in the Scopus database
2-s2.0-85098851523