Some Results for Functions of Kato Class in Domains of Infinite Measure

1989 ◽  
pp. 225-237
Author(s):  
Murali K. Rao
Keyword(s):  
Kato Class ◽  
Infinite Measure

Mean ergodic theorem in function symmetric spaces for infinite measure

2018 ◽  
Vol 2018 (1) ◽  
pp. 35-46
Author(s):  
Vladimir Chilin ◽  
◽  
Aleksandr Veksler ◽  
Keyword(s):  
Ergodic Theorem ◽  
Symmetric Spaces ◽  
Infinite Measure ◽  
Mean Ergodic Theorem

scholarly journals Unique continuation for non-negative solutions of quasilinear elliptic equations

2001 ◽  
Vol 64 (1) ◽  
pp. 149-156 ◽  
Author(s):  
Pietro Zamboni
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equation ◽  
Unique Continuation ◽  
Quasilinear Elliptic Equations ◽  
Kato Class ◽  
Unique Continuation Property ◽  
Continuation Property ◽  
Quasilinear Elliptic

Dedicated to Filippo ChiarenzaThe aim of this note is to prove the unique continuation property for non-negative solutions of the quasilinear elliptic equation We allow the coefficients to belong to a generalized Kato class.

scholarly journals On v-positive type transformations in infinite measure

2015 ◽  
Vol 140 (2) ◽  
pp. 149-170
Author(s):  
Tudor Pădurariu ◽  
Cesar E. Silva ◽  
Evangelie Zachos
Keyword(s):  
Positive Type ◽  
Infinite Measure

Strongly equivalent invariant measures

1980 ◽  
Vol 88 (1) ◽  
pp. 33-43 ◽  
Author(s):  
J. Rosenblatt
Keyword(s):  
Measure Space ◽  
Positive Measure ◽  
Invariant Measures ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Zero Measure ◽  
Infinite Measure ◽  
Two Measures ◽  
Necessary And Sufficient

AbstractTwo measures are strongly equivalent if they have the same sets of zero measure and the same sets of infinite measure. Given a group G of strongly non-singular measurable transformations of a non-atomic positive measure space (X, β, p), if G is amenable, then a necessary and sufficient condition for there to be a G-invariant positive measure on (X, β) which is strongly equivalent to p is that p(E) > 0 implies inf p(gE) > 0 and also p(E) < ∞ implies

scholarly journals CONTINUITY PROPERTIES OF SCHRÖDINGER SEMIGROUPS WITH MAGNETIC FIELDS

2000 ◽  
Vol 12 (02) ◽  
pp. 181-225 ◽  
Author(s):  
KURT BRODERIX ◽  
DIRK HUNDERTMARK ◽  
HAJO LESCHKE
Keyword(s):  
Brownian Bridge ◽  
Integral Kernel ◽  
Dirichlet Boundary Conditions ◽  
Dimensional Euclidean Space ◽  
Kato Class ◽  
Vector Potentials ◽  
Continuity Properties ◽  
Scalar Potentials ◽  
General Configuration ◽  
Zero Vector

The objects of the present study are one-parameter semigroups generated by Schrödinger operators with fairly general electromagnetic potentials. More precisely, we allow scalar potentials from the Kato class and impose on the vector potentials only local Kato-like conditions. The configuration space is supposed to be an arbitrary open subset of multi-dimensional Euclidean space; in case that it is a proper subset, the Schrödinger operator is rendered symmetric by imposing Dirichlet boundary conditions. We discuss the continuity of the image functions of the semigroup and show local-norm-continuity of the semigroup in the potentials. Finally, we prove that the semigroup has a continuous integral kernel given by a Brownian-bridge expectation. Altogether, the article is meant to extend some of the results in B. Simon's landmark paper [Bull. Amer. Math. Soc.7 (1982) 447] to non-zero vector potentials and more general configuration spaces.

scholarly journals Occupation times of sets of infinite measure for ergodic transformations

2005 ◽  
Vol 25 (4) ◽  
pp. 959-976 ◽  
Author(s):  
JON AARONSON ◽  
MAXIMILIAN THALER ◽  
ROLAND ZWEIMÜLLER
Keyword(s):  
Occupation Times ◽  
Infinite Measure ◽  
Ergodic Transformations
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