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Volterra integral equations in Banach space. (English) Zbl 0147.12302


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[1] Shmuel Agmon, On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems, Comm. Pure Appl. Math. 15 (1962), 119 – 147. · Zbl 0109.32701 · doi:10.1002/cpa.3160150203
[2] N. Dunford and J. Schwartz, Linear operators, Part I, Interscience, New York, 1964. · Zbl 0128.34803
[3] Avner Friedman, On integral equations of Volterra type, J. Analyse Math. 11 (1963), 381 – 413. · Zbl 0134.31502 · doi:10.1007/BF02789991
[4] Avner Friedman, Uniqueness of solutions of ordinary differential inequalities in Hilbert space, Arch. Rational Mech. anal. 17 (1964), 353 – 357. · Zbl 0143.16701 · doi:10.1007/BF00250471
[5] Avner Friedman, Periodic behavior of solutions of Volterra integral equations, J. Analyse Math. 15 (1965), 287 – 303. · Zbl 0139.29303 · doi:10.1007/BF02787698
[6] Avner Friedman, Differentiability of solutions of ordinary differential equations in Hilbert space, Pacific J. Math. 16 (1966), 267 – 271. · Zbl 0151.20303
[7] V. P. Gluško and S. G. Kreĭn, Fractional powers of differential operators and imbedding theorems., Dokl. Akad. Nauk SSSR 122 (1958), 963 – 966 (Russian). · Zbl 0089.32503
[8] Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, vol. 31, American Mathematical Society, Providence, R. I., 1957. rev. ed. · Zbl 0078.10004
[9] Tosio Kato, Integration of the equation of evolution in a Banach space, J. Math. Soc. Japan 5 (1953), 208 – 234. · Zbl 0052.12601 · doi:10.2969/jmsj/00520208
[10] Tosio Kato, On linear differential equations in Banach spaces, Comm. Pure Appl. Math. 9 (1956), 479 – 486. · Zbl 0070.34602 · doi:10.1002/cpa.3160090319
[11] Tosio Kato, Fractional powers of dissipative operators, J. Math. Soc. Japan 13 (1961), 246 – 274. · Zbl 0113.10005 · doi:10.2969/jmsj/01330246
[12] Hikosaburo Komatsu, Abstract analyticity in time and unique continuation property of solutions of a parabolic equation, J. Fac. Sci. Univ. Tokyo Sect. I 9 (1961), 1 – 11 (1961). · Zbl 0100.12101
[13] R. S. Phillips, Perturbation theory for semi-groups of linear operators, Trans. Amer. Math. Soc. 74 (1953), 199 – 221. · Zbl 0053.08704
[14] Marvin Shinbrot and Shmuel Kaniel, The initial value problem for the Navier-Stokes equations, Arch. Rational Mech. Anal. 21 (1966), 270 – 285. · Zbl 0148.45504 · doi:10.1007/BF00282248
[15] P. E. Sobolevskiĭ, On equations of parabolic type in a Banach space, Trudy Moscov. Mat. Obšč. 10 (1961), 297-350=Amer. Math. Soc. Transl. (2) 49 (1965), 1-62.
[16] Hiroki Tanabe, A class of the equations of evolution in a Banach space, Osaka Math. J. 11 (1959), 121 – 145. · Zbl 0098.31201
[17] Hiroki Tanabe, Remarks on the equations of evolution in a Banach space, Osaka Math. J. 12 (1960), 145 – 166. · Zbl 0098.31202
[18] Hiroki Tanabe, On the equations of evolution in a Banach space, Osaka Math. J. 12 (1960), 363 – 376. · Zbl 0098.31301
[19] E. C. Titchmarsh, Fourier integrals, Oxford Univ. Press, Oxford, 1950.
[20] Kôsaku Yosida, Fractional powers of infinitesimal generators and the analyticity of the semi-groups generated by them, Proc. Japan Acad. 36 (1960), 86 – 89. · Zbl 0097.31801
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