Fourier Transforms of E-functions of O(5) and G(2)

Háková, Lenka; Hrivnák, Jiří

doi:10.1007/978-3-319-06248-8_21

Cited by 2 publications

(1 citation statement)

References 4 publications

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“…• Discrete orthogonality relations (84) and decomposition formulas (95) are in [8] exemplified for six types of two-variable E−functions of algebras C 2 and G 2 . Effectiveness of interpolation formulas (92) of these two-variable E−functions is demonstrated on complex-valued model functions in [9]. Comparable interpolating ability of real-valued functions is expected for Hartley orbit functions.…”

Section: Discrete Orthogonality Of Orbit Functionsmentioning

confidence: 97%

On discretization of tori of compact simple Lie groups: II

Hrivnák

Patera

2012

J. Phys. A: Math. Theor.

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Ten types of discrete Fourier transforms of Weyl orbit functions are developed. Generalizing one-dimensional cosine, sine and exponential, each type of the Weyl orbit function represents an exponential symmetrized with respect to a subgroup of the Weyl group. Fundamental domains of even affine and dual even affine Weyl groups, governing the argument and label symmetries of the even orbit functions, are determined. The discrete orthogonality relations are formulated on finite sets of points from the refinements of the dual weight lattices. Explicit counting formulas for the number of points of the discrete transforms are deduced. Real-valued Hartley orbit functions are introduced and all ten types of the corresponding discrete Hartley transforms are detailed.

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Section: Discrete Orthogonality Of Orbit Functionsmentioning

confidence: 97%

On discretization of tori of compact simple Lie groups: II

Hrivnák

Patera

2012

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

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On E–discretization of tori of compact simple Lie groups. II

Hrivnák

Juránek

2017

Journal of Mathematical Physics

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Ten types of discrete Fourier transforms of Weyl orbit functions are developed. Generalizing one-dimensional cosine, sine, and exponential, each type of the Weyl orbit function represents an exponential symmetrized with respect to a subgroup of the Weyl group. Fundamental domains of even affine and dual even affine Weyl groups, governing the argument and label symmetries of the even orbit functions, are determined. The discrete orthogonality relations are formulated on finite sets of points from the refinements of the dual weight lattices. Explicit counting formulas for the number of points of the discrete transforms are deduced. Real-valued Hartley orbit functions are introduced, and all ten types of the corresponding discrete Hartley transforms are detailed.

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Fourier Transforms of E-functions of O(5) and G(2)

Cited by 2 publications

References 4 publications

On discretization of tori of compact simple Lie groups: II

On discretization of tori of compact simple Lie groups: II

On E–discretization of tori of compact simple Lie groups. II

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