Szego polynomials and the truncated trigonometric moment problem

We show how Szego polynomials can be used in the theory of truncated trigonometric moment problem.

Nonnegative trigonometric polynomials

An extremal problem for the coefficients of sine polynomials, which are nonnegative in [0,π] , posed and discussed by Rogosinski and Szego is under consideration. An analog of the Fejér-Riesz representation of nonnegative general trigonometric and cosine polynomials is proved for nonnegative sine polynomials. Various extremal sine polynomials for the problem of Rogosinski and Szego are obtained explicitly. Associated cosine polynomials k n (θ) are constructed in such a way that { k n (θ) } are summability kernels. Thus, the L p , pointwise and almost everywhere convergence of the corresponding convolutions, is established. © 2002 Springer-Verlag New York Inc.

Geometrical logarithmic and trigonometric hypercomplex functions of quaternionic type

Quaternionic theory has greatly been developed in recent years [1-12]. Thus, in our view, the study of trigonometric and logarithmic type quaternionic functions is important for the determination and realization of a hyper complex theory. In this paper, we intend to give a geometrical foundation for both logarithmic and trigonometric hyper complex functions based on the exponential function of quaternionic type recently introduced by Borges, Marão and Machado in their paper entitled Geometrical octonions II: Hyper regularity and hyper periodicity of the exponential function appearing. © 2011 Pushpa Publishing House.

Local Trigonometric Methods for Time Series Smoothing.

The thesis is concerned with local trigonometric regression methods. The aim was to develop a method for extraction of cyclical components in time series. The main results of the thesis are the following. First, a generalization of the filter proposed by Christiano and Fitzgerald is furnished for the smoothing of ARIMA(p,d,q) process. Second, a local trigonometric filter is built, with its statistical properties. Third, they are discussed the convergence properties of trigonometric estimators, and the problem of choosing the order of the model. A large scale simulation experiment has been designed in order to assess the performance of the proposed models and methods. The results show that local trigonometric regression may be a useful tool for periodic time series analysis.

Infrared Parallaxes of Young Field Brown Dwarfs and Connections to Directly Imaged Gas-Giant Exoplanets

We have measured high-precision infrared parallaxes with the Canada-France-Hawaii Telescope for a large sample of candidate young (approximate to 10-100 Myr) and intermediate-age (approximate to 100-600 Myr) ultracool dwarfs, with spectral types ranging from M8 to T2.5. These objects are compelling benchmarks for substellar evolution and ultracool atmospheres at lower surface gravities (i.e., masses) than most of the field population. We find that the absolute magnitudes of our young sample can be systematically offset from ordinary (older) field dwarfs, with the young late-M objects being brighter and the young/dusty mid-L (L3-L6.5) objects being fainter, especially at J band. Thus, we conclude the "underluminosity" of the young planetary-mass companions HR 8799b and 2MASS J1207-39b compared to field dwarfs is also manifested in young free-floating brown dwarfs, though the effect is not as extreme. At the same time, some young objects over the full spectral type range of our sample are similar to field objects, and thus a simple correspondence between youth and magnitude offset relative to the field population appears to be lacking. Comparing the kinematics of our sample to nearby stellar associations and moving groups, we identify several new moving group members, including the first free-floating L dwarf in the AB Dor moving group, 2MASS J0355+11. Altogether, the effects of surface gravity (age) and dust content on the magnitudes and colors of substellar objects appear to be degenerate. (C) 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Logarithmic and trigonometric tables.

"Copyright, 1913 and 1920 ... Revised edition published August 1920. Reprinted April, 1924 ... June, 1935."

Logarithmic and trigonometric tables.

Mode of access: Internet.

Third-year mathematics for secondary schools, with Logarithmic and trigonometric tables and mathematical formlas,

Biography on verso of each portrait.

Contributions to a theory of summability of trigonometric integrals.

Bibliography: p. 227.

Parallaxes of 260 stars derived from photographs made at the Leander McCormick observatory,

Mode of access: Internet.

Five-place logarithmic-trigonometric tables.

Mode of access: Internet.

Analysis of trigonometric implicit Runge-Kutta methods

Using generalized collocation techniques based on fitting functions that are trigonometric (rather than algebraic as in classical integrators), we develop a new class of multistage, one-step, variable stepsize, and variable coefficients implicit Runge-Kutta methods to solve oscillatory ODE problems. The coefficients of the methods are functions of the frequency and the stepsize. We refer to this class as trigonometric implicit Runge-Kutta (TIRK) methods. They integrate an equation exactly if its solution is a trigonometric polynomial with a known frequency. We characterize the order and A-stability of the methods and establish results similar to that of classical algebraic collocation RK methods. (c) 2006 Elsevier B.V. All rights reserved.

A solution of the trigonometric moment problem via Tagamlitzki's "Theorem of the Cones"

In 1952 Y. Tagamlitzki gave an elegant proof of the classical Bochner’s theorem on the positively definite functions. Unfortunately, he never published his proof. In this paper we consider a related but simpler problem, the trigonometric moment problem, by using Tagamlitzki’s approach.

On generalized orlicz sequence spaces of Fourier coefficients for trigonometric gap series. I.

We investigate the operator associating with a function fєLp2π, 1trigonometric gap system, as well as an operator from a modular space X ρs(ϕ) to the generalized Orlicz sequence space lϕ.

A Characterization Theorem for the K-functional Associated with the Algebraic Version of Trigonometric Jackson Integrals

2000 Mathematics Subject Classification: 41A25, 41A36.