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The LULU operators, well known in the nonlinear multiresolution analysis of sequences, are extended to functions defined on a continuous domain, namely, a real interval. We show that the extended operators replicate the essential properties of their discrete counterparts. More precisely, they form a fully ordered semi-group of four elements, preserve the local trend and the total variation.
We examine the sum of modified Bessel functions with argument depending quadratically on the summation index given by [S_ u(a)=sum_{ngeq 1} (frac{1}{2} an^2)^{- u} K_ u(an^2)qquad (|arg,a|<pi/2)] as the parameter $|a|to 0$. It is shown that the posit
Let $Pin Bbb Q_p[x,y]$, $sin Bbb C$ with sufficiently large real part, and consider the integral operator $ (A_{P,s}f)(y):=frac{1}{1-p^{-1}}int_{Bbb Z_p}|P(x,y)|^sf(x) |dx| $ on $L^2(Bbb Z_p)$. We show that if $P$ is homogeneous then for each charact
Asymptotic expansions for the Bateman and Havelock functions defined respectively by the integrals [frac{2}{pi}int_0^{pi/2} !!!begin{array}{c} cossinend{array}!(xtan u- u u),du] are obtained for large real $x$ and large order $ u>0$ when $ u=O(|x|)$.
We construct, under the assumption that union of less than continuum many meager subsets of R is meager in R, an additive connectivity function f:R-->R with Cantor intermediate value property which is not almost continuous. This gives a partial answe
In this paper we study the large linear and algebraic size of the family of unbounded continuous and integrable functions in $[0,+infty)$ and of the family of sequences of these functions converging to zero uniformly on compacta and in $L^1$-norm. In