Deduction of L. Hörmander's extension of Ásgeirsson's mean value theorem

L. Hörmander's extension of Ásgeirsson's mean value theorem states that if u is a solution of the inhomogeneous ultrahyperbolic equation (Δ_x−Δ_y)u=f, , , then

     

The left-definite spectral theory for the Dunkl-Hermite differential-difference equation

In this paper, we develop the left-definite spectral theory associated with the self-adjoint operator A_μ in , generated from the Dunkl second-order Hermite differential equation

     

Convergence of cascade algorithms by frequency approach

Starting with an initial function ?₀, the cascade algorithm generates a sequence by cascade operator Qa defined by

     

Bounded perturbations of homogeneous quasilinear operators using bifurcations from infinity

This paper deals with existence results for the following nonlinear problem with the Dirichlet p-Laplacian Δ_p in a bounded domain :

     

On the product of two primitive elements of maximal subfields of a finite field

Let denote a finite field with r elements. Let q be a power of a prime, and p₁,p₂, p₃ be distinct primes. Put

     

Cyclic bandwidth with an edge added

B_c(G) denotes the cyclic bandwidth of graph G. In this paper, we obtain the maximum cyclic bandwidth of graphs of order p with adding an edge as follows:

     

On the residue classes of integer sequences satisfying a linear three term recurrence formula

In this paper we investigate linear three-term recurrence formulae with sequences of integers (T(n))_n?0 and (U(n))_n?0, which are ultimately periodic modulo m, e.g.

     

Maximal functions along surfaces in product spaces

Under certain natural conditions of a measurable radial function , Γ(y₁,y₂)=Γ(|y₁|,|y₂|), we show that the maximal function along surface

     

Bounded positive entire solutions of singular quasilinear elliptic equations

Suppose that β?0 is a constant and that is a continuous function with R₊:=(0,∞). This paper investigates N-dimensional singular, quasilinear elliptic equations of the form

     

The twelfth moment of central values of Hecke series

Let H_j(s) be the Hecke L-function attached to the Maass wave form for the jth eigenvalue of the hyperbolic Laplacian acting in the Hilbert space of automorphic functions for the full modular group. The following mean value estimate for the central values is proved:

     

Pointwise inequalities for ergodic averages and reversed martingales

It is known that the ergodic averages A_n? in the context of the shift action on satisfy pointwise inequalities of the form

     

On the parity of exponents in the standard factorization of n!

Let p₁,p₂,… be the sequence of all primes in ascending order. The following result is proved: for any given positive integer k and any given , there exist infinitely many positive integers n with