# Journal of Mathematical Analysis and Applications

Journal of Mathematical Analysis and Applications > 1995 > 189 > 1 > 215-224

_{l})

_{l}

_{=}<

_{0}be an isotropic random walk on the n-sphere S

^{n}R

^{n}

^{+}

^{1}starting at x

_{0}S

^{n}. Then the random variables X

_{l}cos (Y

_{l}, x

_{0}) form a Markov chain on [-1, 1] whose transition probabilities are closely related to ultraspherical convolutions on [-1, 1]. We prove that √nX

_{l}is normally...

Journal of Mathematical Analysis and Applications > 1995 > 189 > 1 > 85-103

Journal of Mathematical Analysis and Applications > 1995 > 189 > 1 > 128-144

Journal of Mathematical Analysis and Applications > 1995 > 189 > 1 > 179-193

^{2}with the nonlinear exponent approaching infinity. In contrast to the blow-up behavior of the corresponding problem in R

^{n}with n =< 3, the L

^{~}(R

^{2}) norms of the solutions to the equation in R

^{2}remain bounded from below and above. After a careful study on the decay rates of several quantities, we prove that...

Journal of Mathematical Analysis and Applications > 1995 > 189 > 1 > 6-32

Journal of Mathematical Analysis and Applications > 1995 > 189 > 1 > 256-296

^{-}

^{Q}, where Q: R -> R is even, continuous, and of smooth polynomial growth at infinity. Then we call W

^{2}= e

^{-}

^{2}

^{Q}a Freud weight, the most typical examples being W

^{2}

_{β}(x) exp(- x

^{β}), β > 1. Corresponding to the weight W

^{2}, we can form the sequence of orthonormal polynomials {p

_{j}(W

^{2}, x)} ...

Journal of Mathematical Analysis and Applications > 1995 > 189 > 1 > 297-309

Journal of Mathematical Analysis and Applications > 1995 > 189 > 1 > 1-5

Journal of Mathematical Analysis and Applications > 1995 > 189 > 1 > 33-58

Journal of Mathematical Analysis and Applications > 1995 > 189 > 1 > 59-84

Journal of Mathematical Analysis and Applications > 1995 > 189 > 1 > 240-255

Journal of Mathematical Analysis and Applications > 1995 > 189 > 1 > 225-239

Journal of Mathematical Analysis and Applications > 1995 > 189 > 1 > 194-214

Journal of Mathematical Analysis and Applications > 1995 > 189 > 1 > 145-159

Journal of Mathematical Analysis and Applications > 1995 > 189 > 2 > 533-551

^{p}

^{,}

^{r}

_{α}for some 0 < α < 1 and 1 =< p, r =< ~. These conditions are in terms of the Riesz mean of in case 1 =< p =< ~, and in terms of the Dirichlet integral of in case 1 < p < ~. An analogous characterization of periodic functions...