A probabilistic proof for Fourier inversion formula

2018 ◽  
Vol 141 ◽  
pp. 135-142
Author(s):  
Tak Kwong Wong ◽  
Sheung Chi Phillip Yam
Keyword(s):  
Inversion Formula ◽  
Fourier Inversion ◽  
Fourier Inversion Formula ◽  
Probabilistic Proof

scholarly journals A quantum probabilistic approach to Hecke algebras for 𝔭-adic PGL2

2018 ◽  
Vol 21 (03) ◽  
pp. 1850015
Author(s):  
Takehiro Hasegawa ◽  
Hayato Saigo ◽  
Seiken Saito ◽  
Shingo Sugiyama
Keyword(s):  
Inversion Formula ◽  
Probabilistic Approach ◽  
Hecke Algebras ◽  
Hecke Algebra ◽  
Quantum Probability ◽  
Probabilistic Interpretation ◽  
Fourier Inversion ◽  
Fourier Inversion Formula ◽  
The Subject

The subject of the present paper is an application of quantum probability to [Formula: see text]-adic objects. We give a quantum-probabilistic interpretation of the spherical Hecke algebra for [Formula: see text], where [Formula: see text] is a [Formula: see text]-adic field. As a byproduct, we obtain a new proof of the Fourier inversion formula for [Formula: see text].

scholarly journals A Quantum Mechanical Proof of the Fourier Inversion Formula

2011 ◽  
Vol 30 (3) ◽  
pp. 441-457
Author(s):  
Nelson N. de O Castro ◽  
Jacqueline Rojas ◽  
Ramon Mendoza
Keyword(s):  
Inversion Formula ◽  
Quantum Mechanical ◽  
Fourier Inversion ◽  
Fourier Inversion Formula ◽  
Mechanical Proof

scholarly journals On the support of tempered distributions

2010 ◽  
Vol 53 (1) ◽  
pp. 255-270 ◽  
Author(s):  
Jasson Vindas ◽  
Ricardo Estrada
Keyword(s):  
Inversion Formula ◽  
Cesàro Summability ◽  
Fourier Inversion ◽  
Fourier Inversion Formula ◽  
Tempered Distributions ◽  
Tempered Distribution ◽  
Abel Summability ◽  
Open Set ◽  
Cesaro Summability

AbstractWe show that if the summability means in the Fourier inversion formula for a tempered distribution f ∈ S′(ℝn) converge to zero pointwise in an open set Ω, and if those means are locally bounded in L1(Ω), then Ω ⊂ ℝn\supp f. We prove this for several summability procedures, in particular for Abel summability, Cesàro summability and Gauss-Weierstrass summability.

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