Singular Spectrum Analysis is a nonparametric method, which allows one to solve problems like decomposition of a time series into a sum of interpretable components, extraction of periodic components, noise removal and others. In this paper, the algorithm and theory of the SSA method are extended to analyse two-dimensional arrays (e.g. images). The 2D-SSA algorithm based on the SVD of a Hankel-b...

N -th order Hankel Transforms are important for the reconstruction in Magnetic Resonance Imaging (MRI), CAT etc. In this contribution we derive new bounds on functions, which have bandlimited their n-th order Hankel Transform.

In this paper we characterize the kernel of an intermediate Hankel operator on the Bergman space in terms of the inner divisors and obtain a characterization for finite rank intermediate Hankel operators.

In this paper, we obtain the sharp and accurate bounds for logarithmic coefficients of some subclasses analytic functions defined studied in earlier works. Furthermore, second Hankel determinant a class by subordination, such as starlike S*(φ). Some applications our results, which are extensions those reported papers given here special cases. addition, results can be used other popular subclass...

For a single value of `, let f(n, `) denote the number of lattice paths that use the steps (1, 1), (1,−1), and (`, 0), that run from (0, 0) to (n, 0), and that never run below the horizontal axis. Equivalently, f(n, `) satisfies the quadratic functional equation F (x) = P n≥0 f(n, `)x n = 1+ xF (x) + xF (x). Let Hn denote the n by n Hankel matrix, defined so that [Hn]i,j = f(i+ j− 2, `). Here w...

In this paper, we are introducing certain subfamilies of holomorphic functions and making an attempt to obtain upper bound (UB) the second third order Hankel determinants by applying lemmas, Toeplitz determinants, for normalized analytic belong these classes, defined on open unit disc in complex plane. For one inequality, have obtained sharp bound.