Transformations having Continuous Spectrum

Cantor Singular Continuous Spectrum for Operators along Interval Exchange Transformations

It is shown that Schrödinger operators, with potentials along the shift embedding of Lebesgue almost every interval exchange transformations, have Cantor spectrum of measure zero and pure singular continuous for Lebesgue almost all points of the interval.

Continuity of super- and sub-additive transformations of continuous functions

We prove a continuity inheritance property for super- and sub-additive transformations of non-negative continuous multivariate functions defined on the domain of all non-negative points and vanishing at the origin. As a corollary of this result we obtain that super- and sub-additive transformations of continuous aggregation functions are again continuous aggregation functions.

Discrete Spectrum Transformations

An important problem in ergodic theory is to find classifications of various types of measure preserving transformations. An example of this is the theorem of Ornstein that two Bernoulli shifts are isomorphic iff they have the same entropy. So a Bernoulli shift can be assigned a real number that completely determines its isomorphism type. Can this be done for other types of transformations? Per...

On Absolutely Continuous Transformations

Approximately Continuous Transformations

1. An interesting class of real functions of a single real variable, the approximately continuous functions, was introduced by Denjoy [l] in his work on derivatives. The two principal facts discovered by Denjoy are that these functions are of Baire class 1 and have the Darboux property. Ridder [2] showed that the arguments of Denjoy apply to real functions of n variables. In this paper we discu...