Vector valued eigenfunctions of ergodic transformations

A Vector-valued Random Ergodic Theorem

2. Theorem. Let £ be a reflexive B-space and let (S, 2, m) be a a-finite measure space. Let there be defined on S a strongly measurable function Ts with values in the B-space B(H) of bounded linear operators on H. Suppose that || 7\|| ^=1 for all sES. Let h be a measure-preserving transformation (m.p.t.) in (S, 2, m). Then for each XELi(S, £) there is an XELi(S, X) such that limn<„ «_1E"=i T*Th...

Complex Zeros of Real Ergodic Eigenfunctions

We determine the limit distribution (as λ → ∞) of complex zeros for holomorphic continuations φCλ to Grauert tubes of real eigenfunctions of the Laplacian on a real analytic compact Riemannian manifold (M, g) with ergodic geodesic flow. If {φjk} is an ergodic sequence of eigenfunctions, we prove the weak limit formula 1 λj φjk ] → i π∂∂|ξ|g, where φjk ] is the current of integration over the co...

Zeros of real analytic ergodic Laplace eigenfunctions

Ergodic Theory: Nonsingular Transformations

Glossary 1 1. Definition of the subject and its importance 2 2. Basic Results 2 3. Panorama of Examples 8 4. Mixing notions and multiple recurrence 10 5. Topological group Aut(X,μ) 13 6. Orbit theory 15 7. Smooth nonsingular transformations 21 8. Spectral theory for nonsingular systems 22 9. Entropy and other invariants 25 10. Nonsingular Joinings and Factors 27 11. Applications. Connections wi...

On Matrix Transformations concerning the Nakano Vector-valued Sequence Space

We give the matrix characterizations from Nakano vector-valued sequence space (X,p) and Fr (X,p) into the sequence spaces Er , ∞, ∞(q), bs, and cs, where p = (pk) and q = (qk) are bounded sequences of positive real numbers such that pk > 1 for all k∈N and r ≥ 0. 2000 Mathematics Subject Classification. 46A45.