some results on value distribution of the difference operator

Some results on value distribution of the difference operator

In this article, we consider the uniqueness of the difference monomials $f^{n}(z)f(z+c)$. Suppose that $f(z)$ and $g(z)$ are transcendental meromorphic functions with finite order and $E_k(1, f^{n}(z)f(z+c))=E_k(1, g^{n}(z)g(z+c))$. Then we prove that if one of the following holds (i) $n geq 14$ and $kgeq 3$, (ii) $n geq 16$ and $k=2$, (iii) $n geq 22$ and $k=1$, then $f(z)equiv t_1g(z)$ or $f(...

Some difference results on Hayman conjecture and uniqueness

In this paper, we show that for any finite order entire function $f(z)$, the function of the form $f(z)^{n}[f(z+c)-f(z)]^{s}$ has no nonzero finite Picard exceptional value for all nonnegative integers $n, s$ satisfying $ngeq 3$, which can be viewed as a different result on Hayman conjecture. We also obtain some uniqueness theorems for difference polynomials of entire functions sharing one comm...

Some nonexistence results on divisible difference sets

On the fine spectra of the generalized difference operator Delta_{uv} over the sequence space c0

The main purpose of this paper is to detemine the fine spectrum of the generalized difference operator Delta_{uv} over the sequence space c0. These results are more general than the fine spectrum of the generalized difference operator Delta_{uv} of Srivastava and Kumar.

Some Results on the Generalized Gaussian Distribution

For continuous sources the rate-distortion function has been found for a Laplace source with an absolute error distortion d(x, x̂) = |x x̂| [2], exponential source with absolute error distortion [3] and Gaussian source with square error distortion d(x, x̂) = |x x̂|2 [1]. In this paper, we will enlarge this set of known cases by considering the rate-distortion problem for generalized Gaussian (GG) d...

On Some Mean Value Results Involving |ζ(

Several problems involving E(T ) and E2(T ), the error terms in the mean square and mean fourth moment formula for |ζ( 1 2 + it)|, are discussed. In particular it is proved that