By a variant of the standard good λ inequality, we prove the Muckenhoupt-Wheeden inequality for measures which are not necessarily in the Muckenhoupt class. Moreover we can deal with a general potential operator, and consequently we obtain a suitable approach to the two weight inequality for such an operator when one of the weight functions satisfies a reverse doubling condition.
Quantized contact transformations are Toeplitz operators over a contact manifold of the form , where is a Szegö projector, where is a contact transformation and where is a pseudodifferential operator over . They provide a flexible alternative to the Kähler quantization of symplectic maps, and encompass many of the examples in the physics literature, e.g. quantized cat maps and kicked rotors. The index problem is to determine when the principal symbol is unitary, or equivalently to determine...
Dans ce travail, nous considérons un opérateur différentiel simple ainsi que des perturbations. Alors que le spectre de l’opérateur non-perturbé est confiné à une droite à l’intérieur du pseudospectre, nous montrons pour les opérateurs perturbés que les valeurs propres se distribuent à l’intérieur du pseudospectre d’après une loi de Weyl.
In the setting of spaces of homogeneous-type, we define the Integral, , and Derivative, , operators of order , where is a function of positive lower type and upper type less than , and show that and are bounded from Lipschitz spaces to and respectively, with suitable restrictions on the quasi-increasing function in each case. We also prove that and are bounded from the generalized Besov , with , and Triebel-Lizorkin spaces , with , of order to those of order and respectively,...
In this paper we study the resolution problem of an integral equation with operator valued kernel. We prove the equivalence between this equation and certain time varying linear operator system. Sufficient conditions for solving the problem and explicit expressions of the solutions are given.
We analyze some aspects of Mercer's theory when the integral operators act on L²(X,σ), where X is a first countable topological space and σ is a non-degenerate measure. We obtain results akin to the well-known Mercer's theorem and, under a positive definiteness assumption on the generating kernel of the operator, we also deduce series representations for the kernel, traceability of the operator and an integration formula to compute the trace. In this way, we upgrade considerably similar results...
In this paper, we prove that every unbounded linear operator satisfying the Korotkov-Weidmann characterization is unitarily equivalent to an integral operator in L 2(R), with a bounded and infinitely smooth Carleman kernel. The established unitary equivalence is implemented by explicitly definable unitary operators.
Integro-differential equations with time-varying delay can provide us with realistic models of many real world phenomena. Delayed Lotka-Volterra predator-prey systems arise in ecology. We investigate the numerical solution of a system of two integro-differential equations with time-varying delay and the given initial function. We will present an approach based on -step methods using quadrature formulas.