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Displaying 6021 –
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In this paper we study nonlinear second order differential equations subject to separated linear boundary conditions and to linear impulse conditions. Sign properties of an associated Green’s function are investigated and existence results for positive solutions of the nonlinear boundary value problem with impulse are established. Upper and lower bounds for positive solutions are also given.
An operator with infinite dimensional kernel is positive iff it is a positive scalar times a certain product of three projections.
The purpose of this paper is to study the Sarason’s problem on Fock spaces of polyanalytic functions. Namely, given two polyanalytic symbols and , we establish a necessary and sufficient condition for the boundedness of some Toeplitz products subjected to certain restriction on and . We also characterize this property in terms of the Berezin transform.
In 1997 Pták defined generalized Hankel operators as follows: Given two contractions and , an operator is said to be a generalized Hankel operator if and satisfies a boundedness condition that depends on the unitary parts of the minimal isometric dilations of and . This approach, call it (P), contrasts with a previous one developed by Pták and Vrbová in 1988, call it (PV), based on the existence of a previously defined generalized Toeplitz operator. There seemed to be a strong but somewhat...
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