Displaying similar documents to “On the theory of phases of academican O. Borůvka”

Fibration of the phase space for the Korteweg-de Vries equation

Thomas Kappeler (1991)

Annales de l'institut Fourier

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In this article we prove that the fibration of L 2 ( S 1 ) by potentials which are isospectral for the 1-dimensional periodic Schrödinger equation, is trivial. This result can be applied, in particular, to N -gap solutions of the Korteweg-de Vries equation (KdV) on the circle: one shows that KdV, a completely integrable Hamiltonian system, has global action-angle variables.

Rough maximal functions and rough singular integral operators applied to integrable radial functions.

Peter Sjögren, Fernando Soria (1997)

Revista Matemática Iberoamericana

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Let Ω be homogeneous of degree 0 in R and integrable on the unit sphere. A rough maximal operator is obtained by inserting a factor Ω in the definition of the ordinary maximal function. Rough singular integral operators are given by principal value kernels Ω(y) / |y|, provided that the mean value of Ω vanishes. In an earlier paper, the authors showed that a two-dimensional rough maximal operator is of weak type (1,1) when restricted to radial functions. This result is now extended to...