Ruelle operators: functions which are harmonic with respect to a transfer operator

Ruelle Operators: Functions Which Are Harmonic with Respect to a Transfer Operator

Let N ∈ N, N ≥ 2, be given. Motivated by wavelet analysis, we consider a class of normal representations of the C∗-algebra AN on two unitary generators U , V subject to the relation UV U = V N . The representations are in one-to-one correspondence with solutions h ∈ L (T), h ≥ 0, to R (h) = h where R is a certain transfer operator (positivitypreserving) which was studied previously by D. Ruelle...

a comparison of teachers and supervisors, with respect to teacher efficacy and reflection

supervisors play an undeniable role in training teachers, before starting their professional experience by preparing them, at the initial years of their teaching by checking their work within the proper framework, and later on during their teaching by assessing their progress. but surprisingly, exploring their attributes, professional demands, and qualifications has remained a neglected theme i...

On Meromorphic Harmonic Functions with Respect to k-Symmetric Points

Connectedness with Respect to a Closure Operator

A notion of connectedness with respect to a closure operator C and a class of monomorphisms N is introduced in an arbitrary category X . It is shown that under appropriate hypotheses, most classical results about topological connectedness can be generalized to this setting. Examples that illustrate this new concept are provided. Mathematics Subject Classification (1991). 18D35, 06A15, 54D05.

Closure Operators with Respect to a Functor

A notion of closure operator with respect to a functor U is introduced. This allows us to describe a number of mathematical constructions that could not be described by means of the already existing notion of closure operator. Some basic results and examples are provided. Mathematics Subject Classification (1991). 18A22, 18A32, 06A15.