
doi: 10.1007/bf01773383
Given a strongly continuous cosine operator function C on \(R^+\) with values in the Banach algebra B(A) of bounded linear operators in a Banach space A and infinitesimal generator \(\Lambda\), we are concerned with the investigation of the intermediate spaces between A and the domain \(D(\Lambda^ r)\), \(r\in N\), as well as with the characterization of the domains of fractional powers \((-\Lambda)^{\alpha}\), \(0<\alpha
ddc:510, strongly continuous cosine operator function, saturation, non-smooth initial data, Initial value problems for linear higher-order PDEs, regularity of solutions of initial-value problems for second order evolution equations, K-method, intermediate spaces, Weierstrass singular integral, approximate solution of initial-value problems for second order hyperbolic P.D.E.'s by finite difference techniques, Higher-order parabolic equations, Groups and semigroups of linear operators, Regularity of generalized solutions of PDE, domains of fractional powers, Besov spaces, Abstract interpolation of topological vector spaces, moduli of continuity, reduction of well-posed second order problems to equivalent first order ones, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, nonoptimal approximation
ddc:510, strongly continuous cosine operator function, saturation, non-smooth initial data, Initial value problems for linear higher-order PDEs, regularity of solutions of initial-value problems for second order evolution equations, K-method, intermediate spaces, Weierstrass singular integral, approximate solution of initial-value problems for second order hyperbolic P.D.E.'s by finite difference techniques, Higher-order parabolic equations, Groups and semigroups of linear operators, Regularity of generalized solutions of PDE, domains of fractional powers, Besov spaces, Abstract interpolation of topological vector spaces, moduli of continuity, reduction of well-posed second order problems to equivalent first order ones, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, nonoptimal approximation
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