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Imbedding of infinite dimensional distributions into simplified Colombeau type algebras

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Abstract

Using a d-dimensional Gaussian probability space, a simplified Colombeau-type algebra is constructed containing the Meyer-Watanabe distributions. A parallel construction starting by a certain Gelfand triplet also includes the Hida distributions. As an application a new interpretation of the Feynman integrand as a generalized function in our sense is proposed.

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Acknowledgements

The author is indebted to his deceased spouse Sezer Çapar for her constant support and encouragement during the initial stage of preparation of this manuscript and to Professors Yılmaz Akyıldız and Hüsnü Ata Erbay for their helps in different directions. His thanks are also due to the referee for his valuable remarks and suggestions which led to the improvement of the text.

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  1. Sabancı University, Istanbul, Turkey

    Uluğ Çapar

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  1. Uluğ Çapar
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Correspondence to Uluğ Çapar.

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Communicated by Michael Kunzinger.

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Çapar, U. Imbedding of infinite dimensional distributions into simplified Colombeau type algebras. Monatsh Math 199, 755–770 (2022). https://doi.org/10.1007/s00605-022-01692-3

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