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Basis properties of the p, q-sine functions.

Boulton L, Lord GJ - Proc. Math. Phys. Eng. Sci. (2015)

Bottom Line: Our findings rely on a Beurling decomposition of the corresponding change of coordinates in terms of shift operators of infinite multiplicity.We also determine refined bounds on the Riesz constant associated with this family.These results seal mathematical gaps in the existing literature on the subject.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics and Maxwell Institute for Mathematical Sciences , Heriot-Watt University , Edinburgh EH14 4AS, UK.

ABSTRACT

We improve the currently known thresholds for basisness of the family of periodically dilated p,q-sine functions. Our findings rely on a Beurling decomposition of the corresponding change of coordinates in terms of shift operators of infinite multiplicity. We also determine refined bounds on the Riesz constant associated with this family. These results seal mathematical gaps in the existing literature on the subject.

No MeSH data available.


Optimal region of invertibility in lemma 4.1. The horizontal axis is α and the vertical axis is β.
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RSPA20140642F1: Optimal region of invertibility in lemma 4.1. The horizontal axis is α and the vertical axis is β.

Mentions: LetT={β<1, β−α+1>0, β+α+1>0}.LetR1={/α(β+1)/</4β/}∩{β>0}R3={/α(β+1)/</4β/}∩{β<0}R2={/α(β+1)/≥/4β/}=R2∖(R1∪R3).See figure 1.Figure 1.


Basis properties of the p, q-sine functions.

Boulton L, Lord GJ - Proc. Math. Phys. Eng. Sci. (2015)

Optimal region of invertibility in lemma 4.1. The horizontal axis is α and the vertical axis is β.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4309129&req=5

RSPA20140642F1: Optimal region of invertibility in lemma 4.1. The horizontal axis is α and the vertical axis is β.
Mentions: LetT={β<1, β−α+1>0, β+α+1>0}.LetR1={/α(β+1)/</4β/}∩{β>0}R3={/α(β+1)/</4β/}∩{β<0}R2={/α(β+1)/≥/4β/}=R2∖(R1∪R3).See figure 1.Figure 1.

Bottom Line: Our findings rely on a Beurling decomposition of the corresponding change of coordinates in terms of shift operators of infinite multiplicity.We also determine refined bounds on the Riesz constant associated with this family.These results seal mathematical gaps in the existing literature on the subject.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics and Maxwell Institute for Mathematical Sciences , Heriot-Watt University , Edinburgh EH14 4AS, UK.

ABSTRACT

We improve the currently known thresholds for basisness of the family of periodically dilated p,q-sine functions. Our findings rely on a Beurling decomposition of the corresponding change of coordinates in terms of shift operators of infinite multiplicity. We also determine refined bounds on the Riesz constant associated with this family. These results seal mathematical gaps in the existing literature on the subject.

No MeSH data available.