Search Results
You are looking at 1 - 10 of 15 items for
- Author or Editor: S. P. Zhou x
- Refine by Access: All Content x
Abstract
We generalize some old and new results on the determination of jumps of a periodic, Lebesgue integrable function f at each point of discontinuity of first kind in terms of the partial sums of the conjugate series to the Fourier series of f in [1], and in terms of the Abel-Poisson means in [2], to some more general linear operators which satisfy some certain conditions. The linear operators in discussion include the Fejér means, de la Vallée-Poussin means, and Bernstein-Rogosinski sums.
The present note will present a different and direct way to generalize the convexity while keep the classical results for L 1-convergence still alive.
Summary By employing a novel idea and simple techniques, we substantially generalize the Turán type inequality for rational functions with real zeros and prescribed poles established by Min [5] to include L p spaces for 1≤ p ≤ ∞ while loosing the restriction ρ > 2 at the same time.
Abstract
Let f∊L
2π
be a real-valued even function with its Fourier series 
, and let S
n
(f,x) be the nth partial sum of the Fourier series, n≧1. The classical result says that if the nonnegative sequence {a
n
} is decreasing and 
, then 
if and only if 
. Later, the monotonicity condition set on {a
n
} is essentially generalized to MVBV (Mean Value Bounded Variation) condition. Very recently, Kórus further generalized the condition in the classical result to the so-called GM7 condition in real space. In this paper, we give a complete generalization to the complex space.
