Light diffraction by volume Fresnel zone plates (VFZPs) is simulated by the Hankel transform beam propagation method (Hankel BPM). The method utilizes circularly symmetric geometry and small step propagation to calculate the diffracted wave fields by VFZP layers. It is shown that fast and accurate diffraction results can be obtained with the Hankel BPM. The results show an excellent agreement w...

A well-known result from linear system theory states that the minimal inner size of a factorization of the Hankel matrix H of a system gives the minimal order of a realization. In this brief it is shown that when dealing with positive linear systems, the existence of a factorization of the Hankel matrix into two nonnegative matrices is only a necessary condition for the existence of a positive ...

Let La be a Bergman space. We are interested in an intermediate Hankel operator H M φ from La to a closed subspace M of L 2 which is invariant under the multiplication by the coordinate function z. It is well known that there do not exist any nonzero finite rank big Hankel operators, but we are studying same types in case H φ is close to big Hankel operator. As a result, we give a necessary and...

Some well-known authors have extensively used orthogonal polynomials in the framework of geometric function theory. We are motivated by previous research that has been conducted and, this study, we solve Fekete–Szegö problem as well give bound estimates for coefficients and an upper estimate second Hankel determinant functions class G?(v,?) analytical bi-univalent functions, implicating Euler p...

More properties for the translated Whitney numbers of the second kind such as horizontal generating function, explicit formula, and exponential generating function are proposed. Using the translated Whitney numbers of the second kind, we will define the translated Dowling polynomials and numbers. Basic properties such as exponential generating functions and explicit formula for the translated D...

The logarithmic coefficients are very essential in the problems of univalent functions theory. importance is due to fact that bounds on f can transfer Taylor themselves or their powers, via Lebedev–Milin inequalities; therefore, it interesting investigate Hankel determinant whose entries coefficients. main purpose this paper obtain sharp for second strongly starlike and convex functions.

The generalized Motzkin numbers are common generalizations of the Motzkin numbers and the Catalan numbers. We investigate their combinatorial properties, including the combinatorial interpretation, the recurrence relation, the binomial transform, the Hankel transform, the log-convexity, the continued fraction of the generating function, and the total positivity of the corresponding Hankel matrix.