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On abstract parabolic fundamental solutions
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1987 Volume 39 Issue 1 Pages 93-116
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- Published: 1987 Received: December 24, 1984 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Correction information
Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) P. Acquistapace and B. Terreni, Linear parabolic equations in Banach spaces with variable domain but constant interpolation spaces, Annali Scuola Norm. Sup. Pisa Ser. 4, 13 (1986), 75-107.
2) H. Amann, Dual semigroups and second order linear elliptic boundary value problems, Israel J. Math., 45 (1983), 225-254.
3) H. Amann, Existence and regularity for semilinear parabolic evolution equations, Annali Scuola Norm. Sup. Pisa Ser. 4, 11(1984), 593-676.
4) H. Amann, Global existence for semilinear parabolic systems, J. Reine Angew. Math., 360 (1985), 47-83.
5) H. Amann, Quasilinear evolution equations and parabolic systems, Trans. Amer. Math. Soc., 293 (1986), 191-227.
6) J. Bergh and J. Loefstroem, Interpolation Spaces. An Introduction, Springer, Berlin, 1976.
7) G. Da Prato and P. Grisvard, Maximal regularity for evolution equations by interpolation and extrapolation, J. Functional Analysis, 58 (1984), 107-124.
8) E. B. Davies, One-Parameter Semigroups, Academic Press, London, 1980.
9) E. Hille and R. S. Phillips, Functional Analysis and Semi-Groups, Amer. Math. Soc., Providence, R. I., 1957.
10) T. Kato, Abstract evolution equations of parabolic type in Banach and Hilbert spaces, Nagoya Math. J., 19 (1961), 93-125.
11) T. Kato and H. Tanabe, On the abstract evolution equation, Osaka Math. J., 14 (1962), 107-133.
12) H. Komatsu, Fractional powers of operators, Pacific J. Math., 19 (1966), 285-346.
13) H. Komatsu, Fractional powers of operators, VI: Interpolation of non-negative operators and imbedding theorems, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 19 (1972), 1-63.
14) S. G. Krein, Linear Differential Equations in Banach Spaces, Amer. Math. Soc., Providence, R. I., 1972.
15) J. L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications I, Springer, Berlin, 1972.
16) A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983.
17) R. Seeley, Norms and domains of the complex powers AZB Amer. J. Math., 93 (1971), 299-309.
18) R. Seeley, Interpolation in LP with boundary conditions, Studia Math., 44 (1972), 47-60.
19) P. E. Sobolevskii, Equations of parabolic type in a Banach space, Amer. Math. Soc. Transl. Ser. 2, 49 (1966), 1-62.
20) P. E. Sobolevskii, Parabolic equations in a Banach space with an unbounded variable operator, a fractional power of which has a constant domain of definition, Soviet Math. Dokl., 2 (1961), 545-548.
21) H. Tanabe, On the equation of evolution in a Banach space, Osaka Math. J., 12 (1960), 363-376.
22) H. Tanabe, Equations of Evolution, Pitman, London, 1979.
23) H. Tanabe, Note on Volterra integrodifferential equations of parabolic type, Preprint.
24) H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978.
25) A. Yagi, On the abstract linear evolution equations in Banach spaces, J. Math. Soc. Japan, 28 (1976), 290-303.
26) A. Yagi, On the abstract evolution equation of parabolic type, Osaka J. Math., 14 (1977), 557-568.
27) K. Yosida, Functional Analysis, Springer, Berlin, 1965.
Right : [1] P. Acquistapace and B. Terreni, Linear parabolic equations in Banach spaces with variable domain but constant interpolation spaces, Annali Scuola Norm. Sup. Pisa Ser. 4, 13 (1986), 75-107.
[2] H. Amann, Dual semigroups and second order linear elliptic boundary value problems, Israel J. Math., 45 (1983), 225-254.
[3] H. Amann, Existence and regularity for semilinear parabolic evolution equations, Annali Scuola Norm. Sup. Pisa Ser. 4, 11(1984), 593-676.
[4] H. Amann, Global existence for semilinear parabolic systems, J. Reine Angew. Math., 360 (1985), 47-83.
[5] H. Amann, Quasilinear evolution equations and parabolic systems, Trans. Amer. Math. Soc., 293 (1986), 191-227.
[6] J. Bergh and J. Loefstroem, Interpolation Spaces. An Introduction, Springer, Berlin, 1976.
[7] G. Da Prato and P. Grisvard, Maximal regularity for evolution equations by interpolation and extrapolation, J. Functional Analysis, 58 (1984), 107-124.
[8] E. B. Davies, One-Parameter Semigroups, Academic Press, London, 1980.
[9] E. Hille and R. S. Phillips, Functional Analysis and Semi-Groups, Amer. Math. Soc., Providence, R. I., 1957.
[10] T. Kato, Abstract evolution equations of parabolic type in Banach and Hilbert spaces, Nagoya Math. J., 19 (1961), 93-125.
[11] T. Kato and H. Tanabe, On the abstract evolution equation, Osaka Math. J., 14 (1962), 107-133.
[12] H. Komatsu, Fractional powers of operators, Pacific J. Math., 19 (1966), 285-346.
[13] H. Komatsu, Fractional powers of operators, VI: Interpolation of non-negative operators and imbedding theorems, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 19 (1972), 1-63.
[14] S. G. Krein, Linear Differential Equations in Banach Spaces, Amer. Math. Soc., Providence, R. I., 1972.
[15] J. L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications I, Springer, Berlin, 1972.
[16] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983.
[17] R. Seeley, Norms and domains of the complex powers AZB Amer. J. Math., 93 (1971), 299-309.
[18] R. Seeley, Interpolation in LP with boundary conditions, Studia Math., 44 (1972), 47-60.
[19] P. E. Sobolevskii, Equations of parabolic type in a Banach space, Amer. Math. Soc. Transl. Ser. 2, 49 (1966), 1-62.
[20] P. E. Sobolevskii, Parabolic equations in a Banach space with an unbounded variable operator, a fractional power of which has a constant domain of definition, Soviet Math. Dokl., 2 (1961), 545-548.
[21] H. Tanabe, On the equation of evolution in a Banach space, Osaka Math. J., 12 (1960), 363-376.
[22] H. Tanabe, Equations of Evolution, Pitman, London, 1979.
[23] H. Tanabe, Note on Volterra integrodifferential equations of parabolic type, Preprint.
[24] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978.
[25] A. Yagi, On the abstract linear evolution equations in Banach spaces, J. Math. Soc. Japan, 28 (1976), 290-303.
[26] A. Yagi, On the abstract evolution equation of parabolic type, Osaka J. Math., 14 (1977), 557-568.
[27] K. Yosida, Functional Analysis, Springer, Berlin, 1965.
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