A Distributional K Transformation
Armen H. Zemanian · SIAM Journal on Applied Mathematics · 1966
Previous article Next article A Distributional K TransformationA. H. ZemanianA. H. Zemanianhttps://doi.org/10.1137/0114106PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. H. Zemanian, The distributional Laplace and Mellin transformations, SIAM J. Appl. Math., 14 (1966), 41–59 10.1137/0114004 MR0190640 (32:8052) 0147.11903 LinkISIGoogle Scholar[2] A. H. Zemanian, Orthonormal series expansions of certain distributions and distributional transform calculus, J. Math. Anal. Appl., 14 (1966), 263–275 10.1016/0022-247X(66)90026-6 MR0211259 (35:2141) 0138.37804 CrossrefISIGoogle Scholar[3] A. H. Zemanian, Inversion formulas for the distributional Laplace transformation, SIAM J. Appl. Math., 14 (1966), 159–166 10.1137/0114013 MR0190641 (32:8053) 0147.11904 LinkISIGoogle Scholar[4] A. H. Zemanian, A distributional Hankel transformation, SIAM J. Appl. Math., 14 (1966), 561–576 10.1137/0114049 MR0201930 (34:1807) 0154.13803 LinkISIGoogle Scholar[5] A. H. Zemanian, The Hankel transformation of certain distributions of rapid growth, SIAM J. Appl. Math., 14 (1966), 678–690 10.1137/0114056 MR0211211 (35:2093) 0154.13804 LinkISIGoogle Scholar[6] C. S. Meijer, Ueber eine Erweiterung der Laplace-Transformation. I, Nederl. Akad. Wetensch., Proc., 43 (1940), 599–608 MR0002671 (2,96d) 0023.32501 Google Scholar[7] C. S. Meijer, Ueber eine Erweiterung der Laplace-Transformation. II, Nederl. Akad. Wetensch., Proc., 43 (1940), 702–711 MR0002672 (2,96e) 0023.03301 Google Scholar[8] R. P. Boas, Jr., Inversion of a generalized Laplace integral, Proc. Nat. Acad. Sci. U. S. A., 28 (1942), 21–24 MR0005929 (3,233c) 0063.00483 CrossrefGoogle Scholar[9] R. P. Boas, Jr., Generalized Laplace integrals, Bull. Amer. Math. Soc., 48 (1942), 286–294 MR0005928 (3,233b) 0063.00482 CrossrefGoogle Scholar[10] A. Erdélyi, On some functional transformations, Univ. e Politecnico Torino. Rend. Sem. Mat., 10 (1951), 217–234, 1950 MR0047818 (13,937c) 0044.11001 Google Scholar[11] Eugene Jahnke, , Fritz Emde and , Friedrich Lösch, Tables of higher functions, 6th ed. Revised by Friedrich Lösch, McGraw-Hill Book Co., Inc., New York, 1960xiv+318 MR0114317 (22:5140) Google Scholar[12] David Vernon Widder, The Laplace Transform, Princeton Mathematical Series, v. 6, Princeton University Press, Princeton, N. J., 1941x+406 MR0005923 (3,232d) 0063.08245 Google Scholar[13] A. H. Zemanian, A distributional K transformation with applications to time-varying electrical networks, AFCRL-65-789, Tech. Rep., 54, College of Engineering, State University of New York at Stony Brook, 1965 Google Scholar[14] L. Schwartz, Théorie des Distributions, Vol. I, Hermann, Paris, 1957 0078.11003 Google Scholar[15] L. Schwartz, Théorie des Distributions, Vol. II, Hermann, Paris, 1959 0085.09703 Google Scholar[16] Avner Friedman, Generalized functions and partial differential equations, Prentice-Hall Inc., Englewood Cliffs, N.J., 1963xii+340 MR0165388 (29:2672) 0116.07002 CrossrefGoogle Scholar[17] Arthur Erdélyi, , Wilhelm Magnus, , Fritz Oberhettinger and , Francesco G. Tricomi, Higher transcendental functions. Vols. I, II, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953xxvi+302, xvii+396 MR0058756 (15,419i) 0052.29502 Google Scholar[18] A. H. Zemanian, Distribution theory and transform analysis. An introduction to generalized functions, with applications, McGraw-Hill Book Co., New York, 1965xviii+371 MR0177293 (31:1556) 0127.07201 Google Scholar[19] R. V. Churchill, Complex Variables and Applications, McGraw-Hill, New York, 1965 Google Scholar[20] A. Erdélyi, , W. Magnus, , F. Oberhettinger and , F. G. Tricomi, Tables of integral transforms. Vol. II, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1954xvi+451 MR0065685 (16,468c) 0058.34103 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails On The Meijer Transform In SpaceIntegral Transforms and Special Functions, Vol. 10, No. 3-4 Cross Ref On Kμ and Iμ transforms of generalized functionsJournal of Mathematical Analysis and Applications, Vol. 165, No. 1 Cross Ref On K μ Transformation of DistributionsApplicable Analysis, Vol. 42, No. 1-4 Cross Ref The KRÄTZEL Integral Transformation of DistributionsMathematische Nachrichten, Vol. 154, No. 1 Cross Ref An inversion formula for the distributionalH-transformationMathematische Annalen, Vol. 258, No. 4 Cross Ref On the Generalized Hankel and K Transformations20 November 2018 | Canadian Mathematical Bulletin, Vol. 12, No. 6 Cross Ref Volume 14, Issue 6| 1966SIAM Journal on Applied Mathematics History Submitted:05 October 1965Published online:01 August 2006 InformationCopyright © 1966 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0114106Article page range:pp. 1350-1365ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics