Abstract
Let Ep(0) denote the solutions (on 0<R N) of a system P(D) of partial differential equations with constant coefficients in a localizable analytically uniform space E (defined on 0). The relative Kolmogorov diameters of the neighbourhoods of 0 in Ep(0) are estimated from above and below, using the fundamental principle of Ehrenpreis. The diametral dimension, of Ep(0) is calculated and it is proved, that Ep(R N) and Ep(0) are nonisomorphic for (partially) bounded 0, in special cases.
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Dedicated to Heinz-Günter Tillmann on the occasion of his 60th birthday
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Langenbruch, M. Kolmogorov diameters in solution spaces of systems of partial differential equations. Manuscripta Math 53, 35–64 (1985). https://doi.org/10.1007/BF01174010
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DOI: https://doi.org/10.1007/BF01174010