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Liouville’s theorem and Laurent series expansions for solutions of the heat equation

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Abstract

We give a Liouville theorem for entire solutions and Laurent series expansions for solutions with isolated singularities of the heat equation.

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References

  1. Axler, S., Bourdon, P., Ramey, W.: Harmonic Function Theory. Springer, New York (1992)

    Book  MATH  Google Scholar 

  2. Bargmann, V.: On a Hilbert space of analytic functions and an associated integral transform, part I. Commun. Pure Appl. Math. 24, 187–214 (1961)

    Article  MathSciNet  Google Scholar 

  3. Bear, H.S.: Liouville theorems for heat equations. Commun. Partial Differ. Equ. 11, 1605–1625 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  4. Chung, S.Y., Kim, D.: Characterization of temperatute functions with isolated singularity. Math. Nachr. 168, 55–60 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  5. Duan, X.: Poincaré recurrence, second law of thermodynamics and multipliers on the range of the Fourier transform. J. Pseudo Diff. Oper. Appl. 4, 267–277 (2013)

    Article  MATH  Google Scholar 

  6. Fulks, W.: A mean value theorem for the heat equation. Proc. Am. Math. Soc. 17, 6–11 (1966)

    Article  MATH  MathSciNet  Google Scholar 

  7. Gelfand, I.M., Shilov, G.E.: Generalized Functions, vol. II. Academic Press, Boston (1968)

    Google Scholar 

  8. Hirschman, I.I.: A note on the heat equation. Duke Math. J. 19, 487–492 (1952)

    Article  MATH  MathSciNet  Google Scholar 

  9. Hörmander, L.: The Analysis of Linear Partial Differential Operators, vol. I. Springer, New York (1983)

    Google Scholar 

  10. Matsuzawa, T.: A calculus approach to hyperfunctions II. Trans. Am. Math. Soc. 313, 519–654 (1989)

    Article  MathSciNet  Google Scholar 

  11. Kim, J., Wong, M.W.: Invariant mean value property and harmonic functions. Complex Var. Theory Appl. 50, 1049–1059 (2005)

    MATH  MathSciNet  Google Scholar 

  12. Widder, D.V.: The Heat Equation. Academic Press, Boston (1975)

    MATH  Google Scholar 

  13. Wong, M.W.: Partial Differential Equations: Topics in Fourier Analysis. CRC Press, Boca Raton (2014)

    Google Scholar 

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Authors and Affiliations

  1. École Polytechnique Fédérel de Lausanne, Mathematics Building, Section 8, 1015, Lausanne, Switzerland

    Aparajita Dasgupta

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  1. Aparajita Dasgupta
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Correspondence to Aparajita Dasgupta.

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Dasgupta, A. Liouville’s theorem and Laurent series expansions for solutions of the heat equation. J. Pseudo-Differ. Oper. Appl. 5, 539–547 (2014). https://doi.org/10.1007/s11868-014-0103-7

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  • DOI: https://doi.org/10.1007/s11868-014-0103-7

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