Browsing by Subject "Fredholm"
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Item Open Access Aspects of multivariable operator theory on weighted symmetric Fock spaces(World Scientific Publishing, 2014) Kaptanoğlu, H. T.We obtain all Dirichlet spaces Fq, q ∈ ℝ, of holomorphic functions on the unit ball of ℂN as weighted symmetric Fock spaces over ℂN. We develop the basics of operator theory on these spaces related to shift operators. We do a complete analysis of the effect of q ∈ ℝ in the topics we touch upon. Our approach is concrete and explicit. We use more function theory and reduce many proofs to checking results on diagonal operators on the Fq. We pick out the analytic Hilbert modules from among the Fq. We obtain von Neumann inequalities for row contractions on a Hilbert space with respect to each Fq. We determine the commutants and investigate the almost normality of the shift operators. We prove that the C∗-algebras generated by the shift operators on the Fq fit in exact sequences that are in the same Ext class. We identify the groups K0 and K1 of the Toeplitz algebras on the Fq arising in K-theory. Radial differential operators are prominent throughout. Some of our results, especially those pertaining to lower negative values of q, are new even for N = 1. Many of our results are valid in the more general weighted symmetric Fock spaces Fb that depend on a weight sequence b. © World Scientific Publishing Company.Item Open Access The method of analytical regularization in the electromagnetic wave scattering by thin disks(Institution of Engineering and Technology, 2007) Balaban, M. V.; Nosich, A. I.; Altıntaş, Ayhan; Benson, T. M.We consider the problem of diffraction of an arbitrary electromagnetic wave by a thin disk made from different materials and located in free space. Here we imply a zero- thickness perfectly electrically conducting (PEC) disk, and also thin electrically resistive (ER) and dielectric disks whose thickness is much smaller than the disk radius and the free space wavelength, and also much smaller than the skin-layer depth in the ER disk case. The method used for the modeling is based on the integral equation (IE) technique and analytical regularization. Starting with Maxwell's equations, boundary conditions and the radiation condition at infinity we obtain a set of coupled dual IEs (DIEs) for the unknowns and then reduce this set of equations to the coupled IEs of the Fredholm second kind. To verify our results we calculate the far field characteristics in the case of the PEC disk with the incident field being the field of horizontal electrical dipole located on the disk axis.