An Approximation Theorem of Runge Type for the Heat Equation
نویسندگان
چکیده
منابع مشابه
An Approximation Theorem of Runge Type for the Heat Equation
If ft is an open subset of Rn+ , the approximation problem is to decide whether every solution of the heat equation on II can be approximated by solutions defined on all of R . The necessary and sufficient condition on il which insures this type of approximation is that every section of Q taken by hyperplanes orthogonal to the Z-axis be an open set without "holes," i.e., whose complement has no...
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Where ||P ||K = sup{|P (z)| : z ∈ K}. It is known from the Runge approximation theorem that every function which is holomorphic in a neighborhood of compact sets K with K = K̂ can be approximated uniformly on K by analytic polynomials. Our aim here is to prove the same result in the more general situation when the rôle of K̂ is played by the generalized polynomial hull hq(K) introduced by Basener...
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For an infinite-dimensional linear quadratic control problem in Hilbert space, approximation of the solution of the algebraic Riccati operator equation in the strong operator topology is considered under conditions weaker than uniform exponential stability of the approximating systems. As an application, strong convergence of the approximating Riccati operators in case of a previously developed...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1975
ISSN: 0002-9939
DOI: 10.2307/2040146