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Mathematics

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Selected Works

1976

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Weak Type Multipliers For Hankel Transforms, William C. Connett, Alan L. Schwartz Feb 1976

Weak Type Multipliers For Hankel Transforms, William C. Connett, Alan L. Schwartz

UMSL Emeritus

The main result of this paper is that weak type multiplier theorems for Jacobi expansions yield weak type multiplier theorems for Hankel transforms.

In recent papers the authors studied multiplier theorems for ultraspherical and Jacobi expansions. An interesting paper of Igari suggested a new approach to multiplier theorems that used asymptotics instead of the elaborate machinery used earlier.

This paper extends the method of Igari to give the first weak type multiplier theorem for Hankel transforms. This extension is important in itself and because this method together with the authors’ results for Jacobi multipliers will generalize to the “radial” functions …

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Asymptotic Integration Of Linear Differential Equations Subject To Integral Smallness Conditions Involving Ordinary Convergence, William Trench Jan 1976

Asymptotic Integration Of Linear Differential Equations Subject To Integral Smallness Conditions Involving Ordinary Convergence, William Trench

William F. Trench

No abstract provided.

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Topological Properties Of The Real Numbers Object In A Topos, Lawrence Stout Dec 1975

Topological Properties Of The Real Numbers Object In A Topos, Lawrence Stout

Lawrence N. Stout

In his presentation at the categories Session at Oberwolfach in 1973, Tierney defined the continuous reals for a topos with a natural numbers object (he called them Dedekind reals). Mulvey studied the algebraic properties of the object of continuous reals and proved that the construction gave the sheaf of germs of continuous functions from X to R in the spatial topos Sh( X). This paper presents the results of the study of the topological properties of the continuous reals with an emphasis on similarities with classical mathematics and applications to familiar concepts rephrased in topos terms.

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Orthogonal Polynomial Expansions With Nonnegative Coefficients, William F. Trench Dec 1975

Orthogonal Polynomial Expansions With Nonnegative Coefficients, William F. Trench

William F. Trench

No abstract provided.

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