Abstract
Generalized differential operators are ones which agree with differential operators when applied to sufficiently smooth functions but have special symmetry properties which allow them to be defined on less smooth functions. Such operators were used by Cantor [4] in his proof of the uniqueness of representation by trigonometric series and have been an integral part of all extensions of Cantor’s theorem to higher dimensions.
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References
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© 1992 Springer-Verlag New York, Inc.
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Ash, J.M., Cohen, J., Freiling, C., Gatto, A.E., Rinne, D. (1992). Generalized Derivatives. In: Dahlberg, B., Fefferman, R., Kenig, C., Fabes, E., Jerison, D., Pipher, J. (eds) Partial Differential Equations with Minimal Smoothness and Applications. The IMA Volumes in Mathematics and its Applications, vol 42. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2898-1_3
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DOI: https://doi.org/10.1007/978-1-4612-2898-1_3
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