A PSF Approach to Far Field Discretization for Conformal Sources

In this paper we introduce a sampling scheme based on the application of an inverse source problem approach to the far field radiated by a conformal current source. The regularized solution of the problem requires the computation of the Singular Value Decomposition (SVD) of the relevant linear operator, leading to introduce the Point Spread Function in the observation domain, which can be related to the capability of the source to radiate a focusing beam. Then, the application of the Kramer generalized sampling theorem allows introducing a non-uniform discretization of the angular observation domain, tailored to each source geometry. The nearly optimal property of the scheme is compared with the best approximation achievable under a regularized inversion of the pertinent SVD. Numerical results for different two-dimensional curve sources show the effectiveness of the approach with respect to standard sampling approaches with uniform spacing, since it allows to reduce the number of sampling points of the far field.

A PSF Approach to Far Field Discretization for Conformal Sources

In this paper we introduce a sampling scheme based on the application of an inverse source problem approach to the far field radiated by a conformal current source. The regularized solution of the problem requires the computation of the Singular Value Decomposition (SVD) of the relevant linear operator, leading to introduce the Point Spread Function in the observation domain, which can be related to the capability of the source to radiate a focusing beam. Then, the application of the Kramer generalized sampling theorem allows introducing a non-uniform discretization of the angular observation domain, tailored to each source geometry. The nearly optimal property of the scheme is compared with the best approximation achievable under a regularized inversion of the pertinent SVD. Numerical results for different two-dimensional curve sources show the effectiveness of the approach with respect to standard sampling approaches with uniform spacing, since it allows to reduce the number of sampling points of the far field.

Asymptotic properties of Urysohn type generalized sampling operators

The concern of this study is to continue the investigation of convergence properties of Urysohn type generalized sampling operators, which are defined by the author in [Dolomites Res. Notes Approx. 2021, 14 (2), 58-67]. In details, the paper centers around to investigation of the asymptotic properties together with some Voronovskaya-type theorems for the linear and nonlinear counterpart of Urysohn type generalized sampling operators.

On Generalizations of Sampling Theorem and Stability Theorem in Shift-Invariant Subspaces of Lebesgue and Wiener Amalgam Spaces with Mixed-Norms

In this paper, we establish generalized sampling theorems, generalized stability theorems and new inequalities in the setting of shift-invariant subspaces of Lebesgue and Wiener amalgam spaces with mixed-norms. A convergence theorem of general iteration algorithms for sampling in some shift-invariant subspaces of Lp→(Rd) are also given.

On multidimensional Urysohn type generalized sampling operators

<p style='text-indent:20px;'>The concern of this study is to construction of a multidimensional version of Urysohn type generalized sampling operators, whose one dimensional case defined and investigated by the author in [<xref ref-type="bibr" rid="b28">28</xref>] and [<xref ref-type="bibr" rid="b27">27</xref>]. In details, as a continuation of the studies of the author, the paper centers around to investigation of some approximation and asymptotic properties of the aforementioned linear multidimensional Urysohn type generalized sampling operators.</p>

Approximation by pseudo-linear discrete operators

<p style='text-indent:20px;'>In this note, we construct a pseudo-linear kind discrete operator based on the continuous and nondecreasing generator function. Then, we obtain an approximation to uniformly continuous functions through this new operator. Furthermore, we calculate the error estimation of this approach with a modulus of continuity based on a generator function. The obtained results are supported by visualizing with an explicit example. Finally, we investigate the relation between discrete operators and generalized sampling series.</p>

Approximation by sampling-type nonlinear discrete operators in φ-variation

In the present paper, our purpose is to obtain a nonlinear approximation by using convergence in ?-variation. Angeloni and Vinti prove some approximation results considering linear sampling-type discrete operators. These types of operators have close relationships with generalized sampling series. By improving Angeloni and Vinti?s one, we aim to get a nonlinear approximation which is also generalized by means of summability process. We also evaluate the rate of approximation under appropriate Lipschitz classes of ?-absolutely continuous functions. Finally, we give some examples of kernels, which fulfill our kernel assumptions.