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This monograph is devoted to covering the main results in the
qualitative theory of symplectic difference systems, including
linear Hamiltonian difference systems and Sturm-Liouville
difference equations, with the emphasis on the oscillation and
spectral theory. As a pioneer monograph in this field it contains
nowadays standard theory of symplectic systems, as well as the most
current results in this field, which are based on the recently
developed central object - the comparative index. The book contains
numerous results and citations, which were till now scattered only
in journal papers. The book also provides new applications of the
theory of matrices in this field, in particular of the
Moore-Penrose pseudoinverse matrices, orthogonal projectors, and
symplectic matrix factorizations. Thus it brings this topic to the
attention of researchers and students in pure as well as applied
mathematics.
This monograph is devoted to covering the main results in the
qualitative theory of symplectic difference systems, including
linear Hamiltonian difference systems and Sturm-Liouville
difference equations, with the emphasis on the oscillation and
spectral theory. As a pioneer monograph in this field it contains
nowadays standard theory of symplectic systems, as well as the most
current results in this field, which are based on the recently
developed central object - the comparative index. The book contains
numerous results and citations, which were till now scattered only
in journal papers. The book also provides new applications of the
theory of matrices in this field, in particular of the
Moore-Penrose pseudoinverse matrices, orthogonal projectors, and
symplectic matrix factorizations. Thus it brings this topic to the
attention of researchers and students in pure as well as applied
mathematics.
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