Showing papers on "Integrable system published in 1972"
569 citations
62 citations
TL;DR: The space H 1(R n) of integrable functions whose Riesz transforms are integrables was introduced in this article, where the authors considered the problem of preserving singular integral operators in the Lp theory of partial differential equations.
Abstract: It is well-known that the space L 1(Rn ) of integrable functions on Euclidean space fails to be preserved by singular integral operators. As a result the rather large Lp theory of partial differential equations also fails for p = 1. Since L 1 is such a natural space, many substitute spaces have been considered. One of the most interesting of these is the space we will denote by H 1(R n) of integrable functions whose Riesz transforms are integrable.
31 citations
TL;DR: In this article, a family of highly degenerate, nearly integrable, real analytic Hamiltonians of (2n + 2) variables is considered, and it is shown that the system of differential equations associated with the Hamiltonian possesses a quasi-periodic solution with exactly n degrees of freedom (one less than one usually expects to find).
9 citations
Journal Article•
7 citations
TL;DR: In this paper, the authors considered the input-output stability of feedback systems whose forward element is linear and time varying and whose feedback element is a memoryless gain multiplier with a gain that is integrable as a function of time.
Abstract: In this note, we consider the input-output stability of feedback systems whose forward element is linear and time varying and whose feedback element is a memoryless gain multiplier with a gain that is absolutely integrable as a function of time. Necessary and sufficient conditions are derived for the input-output stability of such systems.
3 citations
1 citations