• Corpus ID: 117296179

Scattering, determinants, hyperfunctions in relation to Gamma(1-s)/Gamma(s)

@article{Burnol2006ScatteringDH,
  title={Scattering, determinants, hyperfunctions in relation to Gamma(1-s)/Gamma(s)},
  author={J. F. Burnol},
  journal={arXiv: Number Theory},
  year={2006}
}
  • J. Burnol
  • Published 20 February 2006
  • Mathematics
  • arXiv: Number Theory
The method of realizing certain self-reciprocal transforms as (absolute) scattering, previously presented in summarized form in the case of the Fourier cosine and sine transforms, is here applied to the self-reciprocal transform f(y)-> H(f)(x) = \int_0^\infty J_0(2\sqrt{xy})f(y) dy, which is isometrically equivalent to the Hankel transform of order zero and is related to the functional equations of the Dedekind zeta functions of imaginary quadratic fields. This also allows to re-prove and to… 
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References

SHOWING 1-10 OF 25 REFERENCES
Dualizing the Poisson summation formula.
  • R. Duffin, H. Weinberger
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1991
TLDR
F(x) is the "discrepancy" of phi because it is the error in estimating the integral phi of by its Riemann sum with the constant mesh spacing 1/x.
Two complete and minimal systems associated with the zeros of the Riemann zeta function
We link together three themes which had remained separated so far: the Hilbert space properties of the Riemann zeros, the “dual Poisson formula” of Duffin-Weinberger (also named by us co-Poisson
Zero Spacing Distributions for Differenced L-Functions
The paper studies the local zero spacings of deformations of the Riemann ξ-function under certain averaging and differencing operations. For real h we consider the entire functions Ah(s) := 1 (ξ(s +
The Asymptotics of a Continuous Analogue of Orthogonal Polynomials
Szego polynomials are associated with weight functions on the unit circle. M. G. Krein introduced a continuous analogue of these, a family of entire functions of exponential type associated with a
Fredholm determinants and inverse scattering problems
The Gel'fand-Levitan and Marchenko formalisms for solving the inverse scattering problem are applied together to a single set of scattering phase-shifts. The result is an identity relating two
Spacetime Causality in the Study of the Hankel Transform
Abstract.We study Hilbert space aspects of the Klein-Gordon equation in two-dimensional spacetime. We associate to its restriction to a spacelike wedge a scattering from the past light cone to the
Des équations de Dirac et de Schrödinger pour la transformation de Fourier
On Fourier and Zeta(s)
Abstract We study some of the interactions between the Fourier Transform and the Riemann zeta function (and Dirichlet-Dedekind-Hecke-Tate L-functions).
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