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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Completeness Theorems and Characteristic Matrix Functions - Applications to Integral and Differential Operators (Hardcover, 1st ed. 2022)
Loot Price: R3,910
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Completeness Theorems and Characteristic Matrix Functions - Applications to Integral and Differential Operators (Hardcover, 1st ed. 2022)
Series: Operator Theory: Advances and Applications, 288
Expected to ship within 12 - 19 working days
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This monograph presents necessary and sufficient conditions for
completeness of the linear span of eigenvectors and generalized
eigenvectors of operators that admit a characteristic matrix
function in a Banach space setting. Classical conditions for
completeness based on the theory of entire functions are further
developed for this specific class of operators. The classes of
bounded operators that are investigated include trace class and
Hilbert-Schmidt operators, finite rank perturbations of Volterra
operators, infinite Leslie operators, discrete semi-separable
operators, integral operators with semi-separable kernels, and
period maps corresponding to delay differential equations. The
classes of unbounded operators that are investigated appear in a
natural way in the study of infinite dimensional dynamical systems
such as mixed type functional differential equations, age-dependent
population dynamics, and in the analysis of the Markov semigroup
connected to the recently introduced zig-zag process.
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