A Theorem on Series of Orthogonal Functions with an Application to Strum-Liouville Series

An Extension Theorem with an Application to Formal Tree Series

A grove theory is a Lawvere algebraic theory T for which each hom-set T (n, p) is a commutative monoid; composition on the right distrbutes over all finite sums: ( ∑ i∈F fi) ·h = ∑ i∈F fi ·h. A matrix theory is a grove theory in which composition on the left and right distributes over finite sums. A matrix theory M is isomorphic to a theory of all matrices over the semiring S = M(1, 1). Example...

On absolute generalized Norlund summability of double orthogonal series

In the paper [Y. Okuyama, {it On the absolute generalized N"{o}rlund summability of orthogonal series},Tamkang J. Math. Vol. 33, No. 2, (2002), 161-165] the author has found some sufficient conditions under which an orthogonal seriesis summable $|N,p,q|$ almost everywhere. These conditions are expressed in terms of coefficients of the series. It is the purpose ofthis paper to extend this result...

An Equivalence Theorem for Series of Orthogonal Polynomials.

xj(u, v) = yj(u, v), j = 1, 2, 3, so that again (8) holds. Hence, under our hypotheses, D is mapped isothermically on a spherical surface of finite radius, and circles are not mapped on circles. III. Characterization of Those Isothermic Spherical Maps Which Map Circles on Circles and of Isothermic Maps on Minimal Surfaces.-THEOREM 3. If thefunctions (6) have continuous partial derivatives of th...

A Numerical Integration Method by Using Generalized Series of Functions

A Density Theorem with an Application to Gap Power Series(1) By

Let N be a set of positive integers and let F(z) = I Anz" be an entire function for which An0 (n 0 N). It is reasonable to expect that, if D denotes the density of the set N in some sense, then F(z) will behave somewhat similarly in every angle of opening greater than 2vD. For functions of finite order, the appropriate density seems to be the P6lya maximum density 9. In this paper we introduce ...