Abstract
Weak limits of solutions of boundary value problems for elliptic operators with rapidly oscillating coefficients are, in many important cases, solutions of (sometimes identical) boundary value problems for operators with constant coefficients, phenomenon which is suggestively called “the homogenization” of the partial differential operators involved [1]. Some of the homogenization techniques [5] lead to a natural generalization of Toeplitz operators and to new results concerning the weak limits of inverses of such operators [3].
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References
Bensoussan A., Lions J.L. and Papanicolaou G. Asymptotic Analysis for Periodic Structures, North-Holland, 1978.
Clancey C. and Gohberg I. Factorization Theory for Matrix Valued Functions, Birkhäuser, 1981 (to appear).
Foias C. and Tartar L. Opérateurs de Toeplitz généralisés et homogénéisation. C.R. Acad. Sci., 291 (1980), 1, 15–18.
Lions J.L. Sur quelques questions d’analyse, de mécanique et de controle optimal, Presses Univ. Montrèal, 1976.
Tartar L. Homogeneisation, Cours Peccot, Collège de France, Mars, 1977.
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© 1982 Springer Basel AG
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Foias, C. (1982). Toeplitz Operators and the Theory of Homogenization for Partial Differential Equations. In: Gohberg, I. (eds) Toeplitz Centennial. Operator Theory: Advances and Applications, vol 4. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5183-1_15
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DOI: https://doi.org/10.1007/978-3-0348-5183-1_15
Publisher Name: Birkhäuser, Basel
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