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Hilbert spaces of Hilbert space valued functions

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Part of the Lecture Notes in Mathematics book series (LNM,volume 828)

Keywords

  • Hilbert Space
  • Number Field
  • Positive Definite
  • Linear Manifold
  • Fundamental Variety

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References

  1. N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc. 68(1950), 337–404.

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  2. P. Halmos, A Hilbert space problem book, van Norstrand, New York, 1967.

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  3. E. Hille, Introduction to the general theory of reproducing kernels, Rocky Mountain J. of Math. 2(1971), 321–368.

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  4. E. Hille and R.S. Phillips, Functional analysis and semi-groups, Coll. Pub. Vol. 31, Amer. Math. Soc. Providence R.I, 1957.

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  5. P. Masani, Dilations as propagators of Hilbertian varieties, SIAM J of Math. Anal. 9(1978), 414–456.

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  6. B. Sz.-Nagy, Positive definite kernels generated by operator-valued analytic functions, Acta Sci. Math. 26(1965), 191–192.

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  7. B. Sz.-Nagy and C. Foias, Harmonic analysis of operators on Hilbert space, North Holland, New York, 1970.

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  8. G. B. Pedrick, Theory of reproducing kernels in Hilbert spaces of vector-valued functions, Univ. of Kansas Tech. Rep. 19, Lawrence, 1957.

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  9. J. Rovnyak, Some Hilbert spaces of analytic functions, Dissertation Yale Univ., 1963.

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© 1980 Springer-Verlag

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Burbea, J., Masani, P. (1980). Hilbert spaces of Hilbert space valued functions. In: Weron, A. (eds) Probability Theory on Vector Spaces II. Lecture Notes in Mathematics, vol 828. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097390

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  • DOI: https://doi.org/10.1007/BFb0097390

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10253-3

  • Online ISBN: 978-3-540-38350-5

  • eBook Packages: Springer Book Archive