On the essential approximate point spectrum II
We study the existence of principal eigenvalues for differential operators of second order which are not necessarily in divergence form. We obtain results concerning multiplicity of principal eigenvalues in both the variational and the general case. Our approach uses systematically the Krein-Rutman theorem and fixed point arguments for the inverse of the spectral radius of some associated problems. We also use a variational characterization for both the self-adjoint and the general case.
We deal with several classes of integral transformations of the form where is an operator. In case is the identity operator, we obtain several operator properties on with weights for a generalized operator related to the Fourier cosine and the Kontorovich-Lebedev integral transforms. For a class of differential operators of infinite order, we prove the unitary property of these transforms on and define the inversion formula. Further, for an other class of differential operators of finite...