Boundary Behavior and Cesàro Means of Universal Taylor Series
نویسندگان
چکیده
We study boundary properties of universal Taylor series. We prove that if f is a universal Taylor series on the open unit disk, then there exists a residual subset G of the unit circle such that f is unbounded on all radii with endpoints in G. We also study the effect of summability methods on universal Taylor series. In particular, we show that a Taylor series is universal if and only if its Cesàro means are universal.
منابع مشابه
On the Approximate Properties of Generalized Cesàro Means of Conjugate Trigonometric Fourier Series
The behavior of generalized Cesàro (C, αn)-means (αn ∈ (−1, 0), n = 1, 2, . . . ) of conjugate trigonometric Fourier series of H classes in the space of continuous functions is studied. 2000 Mathematics Subject Classification: 42A50.
متن کاملThe Development and Application of the RCW Method for the Solution of the Blasius Problem
In this research, a numerical algorithm is employed to investigate the classical Blasius equation which is the governing equation of boundary layer problem. The base of this algorithm is on the development of RCW (Rahmanzadeh-Cai-White) method. In fact, in the current work, an attempt is made to solve the Blasius equation by using the sum of Taylor and Fourier series. While, in the most common ...
متن کاملDetermination of a universal series
The known proofs for universal Taylor series do not determine a specific universal Taylor series. In the present paper, we isolate a specific universal Taylor series by modifying the proof in [30]. Thus we determine all Taylor coefficients of a specific universal Taylor series on the disc or on a polygonal domain. Furthermore in non simply connected domains, when universal Taylor series exist, ...
متن کاملSolving the liner quadratic differential equations with constant coefficients using Taylor series with step size h
In this study we produced a new method for solving regular differential equations with step size h and Taylor series. This method analyzes a regular differential equation with initial values and step size h. this types of equations include quadratic and cubic homogenous equations with constant coeffcients and cubic and second-level equations.
متن کاملApproximate solution of the stochastic Volterra integral equations via expansion method
In this paper, we present an efficient method for determining the solution of the stochastic second kind Volterra integral equations (SVIE) by using the Taylor expansion method. This method transforms the SVIE to a linear stochastic ordinary differential equation which needs specified boundary conditions. For determining boundary conditions, we use the integration technique. This technique give...
متن کامل