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  2. Hilbert space - Wikipedia

    en.wikipedia.org/wiki/Hilbert_space

    A Bergman space is an example of a reproducing kernel Hilbert space, which is a Hilbert space of functions along with a kernel K(ζ, z) that verifies a reproducing property analogous to this one. The Hardy space H 2 ( D ) also admits a reproducing kernel, known as the Szegő kernel . [ 37 ]

  3. Bergman kernel - Wikipedia

    en.wikipedia.org/wiki/Bergman_kernel

    where H(D) is the space of holomorphic functions in D. Then L 2,h (D) is a Hilbert space: it is a closed linear subspace of L 2 (D), and therefore complete in its own right. This follows from the fundamental estimate, that for a holomorphic square-integrable function ƒ in D

  4. Quantum configuration space - Wikipedia

    en.wikipedia.org/wiki/Quantum_configuration_space

    The single point denoted in this space is represented by the set of functions () where and represents an index set. In quantum field theory , it is expected that the Hilbert space is also the L 2 {\displaystyle L^{2}} space on the configuration space of the field, which is infinite dimensional, with respect to some Borel measure naturally defined.

  5. Mathematical formulation of quantum mechanics - Wikipedia

    en.wikipedia.org/wiki/Mathematical_formulation...

    As such, quantum states form a ray in projective Hilbert space, not a vector. Many textbooks fail to make this distinction, which could be partly a result of the fact that the Schrödinger equation itself involves Hilbert-space "vectors", with the result that the imprecise use of "state vector" rather than ray is very difficult to avoid. [5]

  6. Linear Operators (book) - Wikipedia

    en.wikipedia.org/wiki/Linear_Operators_(book)

    Linear Operators is a three-volume textbook on the theory of linear operators, written by Nelson Dunford and Jacob T. Schwartz.The three volumes are (I) General Theory; (II) Spectral Theory, Self Adjoint Operators in Hilbert Space; and (III) Spectral Operators.

  7. Reproducing kernel Hilbert space - Wikipedia

    en.wikipedia.org/wiki/Reproducing_kernel_Hilbert...

    Let be an arbitrary set and a Hilbert space of real-valued functions on , equipped with pointwise addition and pointwise scalar multiplication.The evaluation functional over the Hilbert space of functions is a linear functional that evaluates each function at a point ,

  8. Riemann–Hilbert problem - Wikipedia

    en.wikipedia.org/wiki/Riemann–Hilbert_problem

    Another extension of the theory appears in Kamvissis & Teschl (2012) where the underlying space of the Riemann–Hilbert problem is a compact hyperelliptic Riemann surface. The correct factorization problem is no more holomorphic, but rather meromorphic, by reason of the Riemann–Roch theorem.

  9. Kirszbraun theorem - Wikipedia

    en.wikipedia.org/wiki/Kirszbraun_theorem

    The version for Hilbert spaces can for example be found in (Schwartz 1969, p. 21). [2] If H 1 is a separable space (in particular, if it is a Euclidean space) the result is true in Zermelo–Fraenkel set theory; for the fully general case, it appears to need some form of the axiom of choice; the Boolean prime ideal theorem is known to be ...