On Fourier and Hankel Sampling
نویسنده
چکیده
We use the Paley–Wiener theorem for the Fourier and Hankel transforms to compare Fourier and Hankel Sampling.
منابع مشابه
Fast Hankel Transforms
JOHANSEN, H. K., and SORENSEN, K., 1979, Fast Hankel Transforms, Geophysical Prospecting 27, 876-901. Inspired by the linear filter method introduced by D. P. Ghosh in rg7o we have developed a general theory for numerical evaluation of integrals of the Hankel type: m g(r) = Sf(A)hJ,(Ar)dh; v > I. II Replacing the usual sine interpolating function by sinsh (x) = a . sin (xx)/sinh (UTW), where th...
متن کامل1-D Sampling Using Nonuniform Samples and Bessel Functions
We develop the nth order Fourier-Bessel series expansion of 1-D functions in the interval (0,α). Hence we establish the sampling theorem for a function with α-bandlimited nth order Hankel transform. The latter statement implies that the function is also Fourier transform αbandlimited. The samples’ locations are given by the roots of nth order Bessel functions. In addition, the sampling distance...
متن کاملHankel Multipliers and Transplantation Operators
Connections between Hankel transforms of different order for L-functions are examined. Well known are the results of Guy [Guy] and Schindler [Sch]. Further relations result from projection formulae for Bessel functions of different order. Consequences for Hankel multipliers are exhibited and implications for radial Fourier multipliers on Euclidean spaces of different dimensions indicated.
متن کاملCharacterizations of Hankel Multipliers
We give characterizations of radial Fourier multipliers as acting on radial L functions, 1 < p < 2d/(d + 1), in terms of Lebesgue space norms for Fourier localized pieces of the convolution kernel. This is a special case of corresponding results for general Hankel multipliers. Besides L −L bounds we also characterize weak type inequalities and intermediate inequalities involving Lorentz spaces....
متن کاملWiener-hopf plus Hankel Operators on the Real Line with Unitary and Sectorial Symbols
Wiener-Hopf plus Hankel operators acting between Lebesgue spaces on the real line are studied in view of their invertibility, one sided-invertibility, Fredholm property, and the so-called n and d–normal properties. This is done in two different cases: (i) when the Fourier symbols of the operators are unitary functions, and (ii) when the Fourier symbols are related with sectorial elements appear...
متن کامل