Application and Generalization of Convolution Formula

2021 ◽  
Vol 10 (12) ◽  
pp. 4446-4453
Author(s):  
维 谢
Keyword(s):  
Convolution Formula

CONVOLUTION FORMULA AS A STIELTJES RESULTANT

2018 ◽  
Vol 72 (2) ◽  
pp. 429-439
Author(s):  
Soumyarup BANERJEE ◽  
Shigeru KANEMITSU
Keyword(s):  
Convolution Formula

scholarly journals CONVOLUTION FORMULA AND FINITE W BOSON WIDTH EFFECTS IN TOP QUARK WIDTH

2008 ◽  
Vol 23 (22) ◽  
pp. 3525-3533 ◽  
Author(s):  
G. CALDERÓN ◽  
G. LÓPEZ CASTRO
Keyword(s):  
Top Quark ◽  
W Boson ◽  
Matrix Theory ◽  
Finite Width ◽  
Current Limit ◽  
Fermion Masses ◽  
Convolution Formula ◽  
Boson Resonance ◽  
Three Body ◽  
Massless Fermions

In the Standard Model, the top quark decay width Γt is computed from the exclusive t → bW decay. We argue in favor of using the three body decays [Formula: see text] to compute Γt as a sum over these exclusive modes. As dictated by the S-matrix theory, these three body decays of the top quark involve only asymptotic states and incorporate the width of the W boson resonance in a natural way. The convolution formula commonly used to include the finite width effects is found to be valid, in the general case, when the intermediate resonance couples to a conserved current (limit of massless fermions in the case of W bosons). The relation Γt = Γ(t → bW) is recovered by taking the limit of massless fermions followed by the W boson narrow width approximation. Although both calculations of Γt are different at the formal level, their results would differ only by tiny effects induced by light fermion masses and higher-order radiative corrections.

scholarly journals Convolution formula for the sums of generalized Dirichlet $L$-functions

2019 ◽  
Vol 35 (7) ◽  
pp. 1973-1995
Author(s):  
Olga Balkanova ◽  
Dmitry Frolenkov
Keyword(s):  
Convolution Formula ◽  
Generalized Dirichlet

scholarly journals Aumann Fuzzy Improper Integral and Its Application to Solve Fuzzy Integro-Differential Equations by Laplace Transform Method

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Elhassan Eljaoui ◽  
Said Melliani ◽  
L. Saadia Chadli
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
Convolution Type ◽  
Convolution Product ◽  
Fuzzy Mapping ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Improper Integral ◽  
Convolution Formula

We introduce the Aumann fuzzy improper integral to define the convolution product of a fuzzy mapping and a crisp function in this paper. The Laplace convolution formula is proved in this case and used to solve fuzzy integro-differential equations with kernel of convolution type. Then, we report and correct an error in the article by Salahshour et al. dealing with the same topic.

A convolution involving Bell polynomials

1973 ◽  
Vol 74 (1) ◽  
pp. 97-106 ◽  
Author(s):  
G. P. M. Heselden
Keyword(s):  
Bell Polynomials ◽  
Special Polynomial ◽  
Convolution Formula

AbstractA convolution formula is established for Bell polynomials. This is expressed in seven equivalent ways and used to derive further properties of these polynomials. The application of these results to some twenty-seven special polynomial sets is shown and illustrated in the case of binomial, Hermite, Gegenbauer and generalized Bernoulli sets.

scholarly journals On the Tensor Convolution and the Quantum Separability Problem

2010 ◽  
Vol 17 (04) ◽  
pp. 331-346
Author(s):  
Gabriel Pietrzkowski
Keyword(s):  
Abelian Group ◽  
Tensor Product ◽  
Hermitian Operator ◽  
Product Formula ◽  
Locally Compact Abelian Group ◽  
Locally Compact ◽  
Equivalent Problem ◽  
Finite Dimensional ◽  
Separability Problem ◽  
Convolution Formula

We consider the problem of separability: decide whether a Hermitian operator on a finite dimensional Hilbert tensor product [Formula: see text] is separable or entangled. We show that the tensor convolution [Formula: see text] defined for mappings [Formula: see text] on an almost arbitrary locally compact abelian group G , gives rise to formulation of an equivalent problem to the separability one.

scholarly journals Some Convolution Formulae Related to the Second-Order Linear Recurrence Sequence

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 788 ◽  
Author(s):  
Zhuoyu Chen ◽  
Lan Qi
Keyword(s):  
Power Series Expansion ◽  
Second Order ◽  
Linear Recurrence ◽  
Recurrence Sequence ◽  
Order Linear ◽  
Symmetry Properties ◽  
Elementary Methods ◽  
Linear Recurrence Sequence ◽  
Convolution Formula ◽  
The Relationship

The main aim of this paper is that for any second-order linear recurrence sequence, the generating function of which is f ( t ) = 1 1 + a t + b t 2 , we can give the exact coefficient expression of the power series expansion of f x ( t ) for x ∈ R with elementary methods and symmetry properties. On the other hand, if we take some special values for a and b, not only can we obtain the convolution formula of some important polynomials, but also we can establish the relationship between polynomials and themselves. For example, we can find relationship between the Chebyshev polynomials and Legendre polynomials.

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