caa a22 4500 467932034 CHVBK 20180406152946.0 cr unu---uuuuu 170328e20060101xx s 000 0 eng 10.1007/s00020-004-1336-2 doi (NATIONALLICENCE)springer-10.1007/s00020-004-1336-2 Harper Zen School of Mathematics, University of Leeds, LS2 9JT, Leeds, United Kingdom aut Applications of the Discrete Weiss Conjecture in Operator Theory [Elektronische Daten] [Zen Harper] Abstract.: In this paper, we study a discrete version of the Weiss Conjecture. In Section 1 we discuss the Reproducing Kernel Thesis and in Section 2 we introduce the operators which concern us. Section 3 shows how to relate these operators to Carleson embeddings and weighted composition operators, so that we can apply the Carleson measure theorem to obtain conditions for boundedness and compactness of many weighted composition operators. Section 4 contains Theorem 4.4 which is a discrete version of the Weiss Conjecture for contraction semigroups, and finally Section 5 shows how the usual (continuous time) Weiss Conjecture is related to the discrete version studied here; in fact they are equivalent (for scalar valued observation operators). The main advantage of the discrete version is that it is technically simpler - the observation operators are automatically bounded and the functional calculus can be achieved using power series. Birkhäuser Verlag, Basel, 2006 Hankel operators nationallicence Carleson embeddings nationallicence composition operators nationallicence Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhauser.ch 54/1(2006-01-01), 69-88 0378-620X 54:1<69 2006 54 20 https://doi.org/10.1007/s00020-004-1336-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00020-004-1336-2 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Harper Zen School of Mathematics, University of Leeds, LS2 9JT, Leeds, United Kingdom aut NATIONALLICENCE 773 0- Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhauser.ch 54/1(2006-01-01), 69-88 0378-620X 54:1<69 2006 54 20 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer