Generalized functions with pseudobounded support in constructive mathematics
In this paper we define pseudoboundedness for support of a distribution which is weaker than boundedness in Bishop's constructive mathematics. We prove in Bishop's framework that a distribution (sequentially continuous linear functional on the space D(R) of test functions) with pseudobounded support is a sequentially continuous linear functional on the space epsilon(R) of infinitely differentiable functions on R. We also show that the following three propositions can be proved in classical mathematics, Brouwer's intuitionistic mathematics and constructive recursive mathematics of Markov's school, but cannot be in Bishop's framework: every sequentially continuous linear functional on epsilon(R) is bounded on epsilon(R) every bounded distribution with pseudobounded support is bounded on epsilon(R); every sequentially continuous linear functional on epsilon(R) is a distribution with compact support. (C) 2006 Published by Elsevier Inc.
pseudobounded support constructive mathematics boundedness distribution sequential continuity bd-n