×

Distributional boundary values in \({\mathcal D}'_{L^{p}}\). II. (English) Zbl 0229.46042


MSC:

46F20 Distributions and ultradistributions as boundary values of analytic functions
46F12 Integral transforms in distribution spaces
PDFBibTeX XMLCite
Full Text: Numdam EuDML

References:

[1] Carmichael , Richard D. : Distributional Boundary Values in D’Lp , Rendiconti Sem. Mat. Università di Padova , 43 ( 1970 ), pp. 35 - 53 . Numdam | MR 278064 | Zbl 0235.46063 · Zbl 0235.46063
[2] Hille , E. , and Tamarkin , J.D. : On a Theorem of Paley and Wiener , Annals of Math. , 34 ( 1933 ), pp. 606 - 614 . MR 1503128 | JFM 59.0424.01 · JFM 59.0424.01
[3] Hille , E. , and Tamarkin , J.D. : A Remark on Fourier Transforms and Functions Analytic in a Half-Plane , Compositio Math. , 1 ( 1934 ), pp. 98 - 102 . Numdam | JFM 60.0347.01 · Zbl 0008.30602
[4] Tillmann , H.G. : Distributionen als Randverteilungen analytischer Funktionen. II , Math. Zeitschift , 76 ( 1961 ), pp. 5 - 21 . MR 125441 | Zbl 0097.09603 · Zbl 0097.09603 · doi:10.1007/BF01210955
[5] Luszczki , Z. , and Zielezny , Z. : Distributionen Der Raume D’Lp Als Randverteilungen Analytischer Funktionen , Colloquim Math. , 8 ( 1961 ), pp. 125 - 131 . Article | MR 126718 | Zbl 0201.16401 · Zbl 0201.16401
[6] Beltrami , E.J. , and Wohlers , M.R. : Distributional Boundary Value Theorems and Hilbert Transforms , Arch. Rational Mech. Anal. , 18 ( 1965 ), pp. 304 - 309 . MR 179611 | Zbl 0151.18204 · Zbl 0151.18204 · doi:10.1007/BF00251669
[7] Beltrami , E.J. , and Wohlers , M.R. : Distributional Boundary Values of Functions Holomorphic in a Half Plane , J. Math. Mech. , 15 ( 1966 ), pp. 137 - 146 . MR 193246 | Zbl 0151.18301 · Zbl 0151.18301
[8] Beltrami , E.J. , and Wohlers , M.R. : Distributions and the Boundary Values of Analytic Functions , Academic Press , New York , 1966 . MR 208362 | Zbl 0186.19202 · Zbl 0186.19202
[9] Beltrami , E.J. , and Wohlers , M.R. : The Cauchy Integral of Tempered Distributions and Some Theorems on Analytic Continuation , SIAM J. Appl. Math. , 15 ( 1967 ), pp. 1077 - 1087 . MR 236361 | Zbl 0164.15501 · Zbl 0164.15501 · doi:10.1137/0115092
[10] Schwartz , L. : Théorie des Distributions , Hermann , Paris , 1966 . MR 209834 | Zbl 0962.46025 · Zbl 0962.46025
[11] Hörmander , L. : Linear Partial Differential Operators , Springer-Verlag , Berlin , 1963 . MR 404822 | Zbl 0108.09301 · Zbl 0108.09301
[12] Vladimirov , V.S. : Methods of the Theory of Functions of Several Complex Variables , M.I.T. Press , Cambridge, Mass. , 1966 . MR 201669
[13] Carmichael , Richard D. : Functions Analytic in an Octant and Boundary Values of Distributions , J. Math. Analysis Appl. , to appear 1971 . MR 283566 | Zbl 0201.45001 · Zbl 0201.45001 · doi:10.1016/0022-247X(71)90081-3
[14] Hoffman , Kenneth : Banach Spaces of Analytic Functions , Prentice-Hall , Englewood Cliffs, N. J. , 1962 . MR 133008 | Zbl 0734.46033 · Zbl 0734.46033
[15] Titchmarsh , E.C. : Introduction to the Theory of Fourier Integrals , 2 nd. Edition, Oxford Press , London , 1948 . JFM 63.0367.05 · JFM 63.0367.05
[16] Hille , E. : Analytic Function Theory , Vol. II , Ginn and Company , New York , 1962 . MR 201608 | Zbl 0102.29401 · Zbl 0102.29401
[17] Zygmund , A. : On the Boundary Values of Functions of Several Complex Variables , Fundamenta Math. , 36 ( 1949 ), pp. 207 - 235 . Article | MR 35832 | Zbl 0040.19201 · Zbl 0040.19201
[18] Zygmund , A. : Trigometric Series, Vols. I and II, 2nd. Edition , Cambridge University Press , London , 1968 . MR 236587
[19] Bremermann , H. : Distributions, Complex Variables, and Fourier Transforms , Addison-Wesley , Reading, Mass. , 1965 . MR 208364 | Zbl 0151.18102 · Zbl 0151.18102
[20] Carmichael , Richard D. : Distributions as the Boundary Values of Analytic Functions , Proc. Japan Acad. , 45 ( 1969 ), pp. 861 - 865 . Article | MR 262819 | Zbl 0198.46505 · Zbl 0198.46505 · doi:10.3792/pja/1195520549
[21] Carmichael , Richard D. : Distributional Boundary Values of Functions Analytic in Tubular Radial Domains , Indiana U. Math. J. (formely J. Math. Mech. ), to appear April, 1971 . MR 414918 | Zbl 0207.12403 · Zbl 0207.12403 · doi:10.1512/iumj.1971.20.20066
[22] Bochner , S. , and Martin , W.T. : Several Complex Variables , Princeton University Press , Princeton, N. J. , 1948 . MR 27863 | Zbl 0041.05205 · Zbl 0041.05205
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.