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Earlier work found that goldfish (Carassius auratus) acquire a conditioned avoidance shuttle response (CASR) differentially as a function of CS location (same, opposite, or both tank ends) when the CS is a sudden onset of illumination, and hypothesized that subjects acquire an aversion to the light. The present study finds no evidence for a conditioned aversion, but shows initial negative phototactic effects in the onset illumination situation which occurs without acquisition. Additionally, when the localized CS is a color change rather than an illumination change, the differential effects between same and both do not occur, and the very low CASR …

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 …