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The aim of the present book is to propose a new algebraic approach
to the study of norm stability of operator sequences which arise,
for example, via discretization of singular integral equations on
composed curves. A wide variety of discretization methods,
including quadrature rules and spline or wavelet approximations, is
covered and studied from a unique point of view. The approach takes
advantage of the fruitful interplay between approximation theory,
concrete operator theory, and local Banach algebra techniques. The
book is addressed to a wide audience, in particular to
mathematicians working in operator theory and Banach algebras as
well as to applied mathematicians and engineers interested in
theoretical foundations of various methods in general use,
particularly splines and wavelets. The exposition contains numerous
examples and exercises. Students will find a large number of
suggestions for their own investigations.
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