47
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Singularities in space-time foam algebras

Pages 1763-1774 | Received 28 Feb 2010, Accepted 04 Jul 2010, Published online: 21 Sep 2010

References

  • Schwartz , L . 1954 . Sur l'impossibilite de la multiplications des distributions . C. R. Acad. Sci. Paris , 239 : 847 – 848 .
  • Rosinger , EE . 1966 . Imbedding of the 𝒟′ distributions into pseudotopological algebras . Stud. Cerc. Mat. , 18 : 687 – 729 .
  • Rosinger , EE . 1968 . Pseudotopological spaces: Imbedding of the 𝒟′ distributions into algebras . Stud. Cerc. Mat. , 20 : 553 – 582 .
  • Rosinger , EE . 1978 . Distributions and Nonlinear Partial Differential Equations, Springer Lecture Notes in Mathematics , Vol. 684 , Berlin : Springer .
  • Rosinger , EE . 1980 . Nonlinear Partial Differential Equations, Sequential and Weak Solutions, North Holland Mathematics Studies , Vol. 44 , Amsterdam : North Holland .
  • Rosinger , EE . 1987 . Generalized Solutions of Nonlinear Partial Differential Equations, North Holland Mathematics Studies , Vol. 146 , Amsterdam : North Holland .
  • Rosinger , EE . 1990 . Nonlinear Partial Differential Equations, An Algebraic View of Generalized Solutions, North Holland Mathematics Studies , Vol. 164 , Amsterdam : North Holland .
  • Colombeau , JF . 1984 . New Generalized Functions and Multiplication of Distributions, North Holland Mathematics Studies , Vol. 84 , Amsterdam : North Holland .
  • Colombeau , JF . 1985 . Elementary Introduction to New Generalized Functions, North Holland Mathematics Studies , Vol. 113 , Amsterdam : North Holland .
  • Adamczewski , M , Colombeau , JF and Le Roux , AY . 1990 . Convergence of numerical schemes involving powers of the Dirac delta function . J. Math. Anal. Appl. , 145 : 172 – 185 .
  • Bernard , S , Colombeau , JF , Meril , A and Remaki , L . 2001 . Conservation laws with discontinuous coefficients . J. Math. Anal. Appl. , 258 : 63 – 86 .
  • Colombeau , JF and Heibig , A . 1994 . Generalized solutions to Cauchy problems . Monatsh. Math. , 117 : 33 – 49 .
  • Colombeau , JF , Heibig , A and Oberguggenberger , M . 1996 . Generalized solutions to partial differential equations of evolution type . Acta Appl. Math. , 45 : 115 – 142 .
  • Grosser , M , Kunzinger , M , Obergugenberger , MB , Steinbauer , R and Vickers , J . 2002 . Geometric Theory of Generalized Functions with Applications to General Relativety , Dordrecht : Kluwer Academic Publishers .
  • Obergugenberger , MB . 1992 . Multiplication of Distributions and Applications to Partial Differential Equations , Harlow : Longman .
  • Oberguggenberger , MB , Pilipovic , S and Scarpalezos , D . 2003 . Local properties of Colombeau generalized functions . Math. Nachr. , 256 : 88 – 99 .
  • Rosinger , EE . 2001 . How to solve smooth nonlinear PDEs in algebras of generalized functions with dense singularities . Appl. Anal. , 78 : 355 – 378 .
  • Rosinger , EE . 2007 . Differential algebras with dense singularities on manifolds . Acta Appl. Math. , 95 : 233 – 256 .
  • E.E. Rosinger, Space-time foam differential algebras of generalized functions and a Global Cauchy–Kovalevskaia theorem, Acta Appl. Math 109 (2010), pp. 439–462
  • Vernaeve , H . 2003 . Embedding distributions in algebras of generalized functions with singularities . Monatsh. Math. , 138 : 307 – 318 .
  • Mallios , A and Rosinger , EE . 2001 . Space-time foam dense singularities and de Rham cohomology . Acta Appl. Math. , 67 : 59 – 89 .
  • Oxtoby , JC . 1980 . Meaure and Category, , 2nd , Berlin : Springer-Verlag .
  • Berberian , S . 1974 . Lectures in Functional Analysis and Operator Theory, Graduate Texts in Mathematics , Vol. 15 , Berlin : Springer-Verlag .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.