28,578 research outputs found
Geometric properties of the complex Baskakov-Stancu operators in the unit disk
In this article, we determine certain conditions under which the partial sums involving thecomplex Baskakov-Stancu operators of analytic univalent functions of bounded turning are also of boundedturning. Moreover, we consider some geometric properties such as starlikeness and convexity for these partialsums. The lower bound of the partial sums of univalent functions is computed using the lower bound of thecomplex Baskakov-Stancu operators of analytic function
Orthogonal polynomials of discrete variable and boundedness of Dirichlet kernel
For orthogonal polynomials defined by compact Jacobi matrix with exponential
decay of the coefficients, precise properties of orthogonality measure is
determined. This allows showing uniform boundedness of partial sums of
orthogonal expansions with respect to norm, which generalize
analogous results obtained for little -Legendre, little -Jacobi and
little -Laguerre polynomials, by the authors
Bounds for the covariance of functions of infinite variance stable random variables with applications to central limit theorems and wavelet-based estimation
We establish bounds for the covariance of a large class of functions of infinite variance stable random variables, including unbounded functions such as the power function and the logarithm. These bounds involve measures of dependence between the stable variables, some of which are new. The bounds are also used to deduce the central limit theorem for unbounded functions of stable moving average time series. This result extends the earlier results of Tailen Hsing and the authors on central limit theorems for bounded functions of stable moving averages. It can be used to show asymptotic normality of wavelet-based estimators of the self-similarity parameter in fractional stable motions
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