Two-direction multiwavelet moments

Kwon, Soon-Geol

doi:10.1016/j.amc.2012.09.034

Cited by 7 publications

(7 citation statements)

References 9 publications

(24 reference statements)

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“…An algorithm for computing continuous moments of the two-direction multiscaling function φ and multiwavelets ψ was derived in [8]. Continuous moments of φ and ψ can be computed if the recurrence coefficients of φ and ψ are given.…”

Section: Two-direction Multiscaling Functions and Multiwaveletsmentioning

confidence: 99%

“…Continuous moments of φ and ψ can be computed if the recurrence coefficients of φ and ψ are given. Here we review some results for moments derived from [8].…”

Section: Two-direction Multiscaling Functions and Multiwaveletsmentioning

confidence: 99%

“…Two-direction multiscaling functions φ and two-direction multiwavelets ψ associated with φ, which are more general setting than one-direction multiscaling functions and multiwavelets, have been investigated in a few papers in the literature, for example, see [3,5,8,11,12,16,17,18]. The two-direction setting is more flexible than one-direction setting.…”

Section: Introductionmentioning

confidence: 99%

“…By (2.17) and(2.19) (detailed computation can be found in[8, Example 4.2]), the jth continuous moments m j of φ for j = 0, 1, 2 are…”

mentioning

confidence: 99%

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Point Values and Normalization of Two-Direction Multi-wavelets and their Derivatives

Keinert

Kwon

2015

Kyungpook mathematical journal

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Abstract. A two-direction multiscaling function φ satisfies a recursion relation that uses scaled and translated versions of both itself and its reverse. This offers a more general and flexible setting than standard one-direction wavelet theory. In this paper, we investigate how to find and normalize point values and derivative values of two-direction multiscaling and multiwavelet functions. Determination of point values is based on the eigenvalue approach. Normalization is based on normalizing conditions for the continuous moments of φ. Examples for illustrating the general theory are given.

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Section: Two-direction Multiscaling Functions and Multiwaveletsmentioning

confidence: 99%

“…Continuous moments of φ and ψ can be computed if the recurrence coefficients of φ and ψ are given. Here we review some results for moments derived from [8].…”

Section: Two-direction Multiscaling Functions and Multiwaveletsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…By (2.17) and(2.19) (detailed computation can be found in[8, Example 4.2]), the jth continuous moments m j of φ for j = 0, 1, 2 are…”

mentioning

confidence: 99%

See 2 more Smart Citations

Point Values and Normalization of Two-Direction Multi-wavelets and their Derivatives

Keinert

Kwon

2015

Kyungpook mathematical journal

Self Cite

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show abstract

“…The recursion coefficients p k are scalars. Two-direction scaling function ϕ and wavelet function ψ, which are a more general setting than the one-direction scaling function and wavelet, are investigated in [2,3,4,5,6,7].…”

Section: Introductionmentioning

confidence: 99%