Abstract
Ultradistributions of Beurling type D’(M p ), L s ) and of Roumieu type D’({M p }, Ls) are defined where M p , p = 0,1,2,3,..., is a sequence of positive real numbers which is used to define ultradistributions. A norm growth of the Cauchy integral of elements in D’ (*,L S), where * is either (M p ) or {M p }, is obtained involving the associated function M*(p) corresponding to the sequences M p ; the Cauchy integral is a holomorphic function of z ∊ n + iC 2282 ℛ n where C is a regular cone in ℛ n. We define holomorphic functions in tubes ℛ n + iC which are motivated by this norm growth and show that these functions are representable by Fourier-Laplace transforms; certain of these functions obtain ultradistributional boundary values. Problems for future research are indicated.
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© 1993 Springer Science+Business Media New York
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Carmichael, R.D., Pathak, R.S., Pilipović, S. (1993). Ultradistributional Boundary Values of Holomorphic Functions. In: Pathak, R.S. (eds) Generalized Functions and Their Applications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1591-7_2
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DOI: https://doi.org/10.1007/978-1-4899-1591-7_2
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-1593-1
Online ISBN: 978-1-4899-1591-7
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