hilbert space in English

noun
1
an infinite-dimensional analog of Euclidean space.
His theorem, now called the Riesz - Fischer theorem, which he proved in 1907, is fundamental in the Fourier analysis of Hilbert space .

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Below are sample sentences containing the word "hilbert space" from the English Dictionary. We can refer to these sentence patterns for sentences in case of finding sample sentences with the word "hilbert space", or refer to the context using the word "hilbert space" in the English Dictionary.

1. Her dissertation, Stochastic Differential Equations In A Hilbert Space, was supervised by Peter Falb.

2. The Borel functional calculus extends to unbounded self-adjoint operators on a Hilbert space.

3. First an abstract Hilbert space model is developed as a general framework for problems of this type.

4. 29 This paper gives a part of useful conclusions of separable Hilbert space and proves to it.

5. Therefore the Adjoint can only be defined on another subset of the Hilbert space, the domain of the Adjoint

6. C.6 Adjoints for Operators on a Hilbert Space 251 Hence D = D as an operator mapping S into L2(R)

7. The existence of the eigenfrequencies arises from the theory of the completely continuous self-adjoint operators in an Hilbert space.

8. Furthermore it is shown, that this method yields an admissible sequence of directions in case of a quadratic minimization problem in Hilbert space.

9. Equilibrium fluctuations of dynamic quantities and the associated spectral amplitudes can be regarded as stationary functions and orthogonal measures, respectively, with values in a Hilbert space.

10. A measure that takes values in the set of self-adjoint projections on a Hilbert space is called a projection-valued measure; these are used in functional analysis for the spectral theorem.

11. (In the most general cases, the domain of the Adjoint can be a much, much smaller set [even finite dimensional], so does not make much sense as an operator on the original Hilbert space.

12. It can be shown that if L and L* are linear operators in a Hilbert space for which (.x, Ly) = (L*x, y) for all x, y in H, then L is bounded and L* is the Adjoint …

13. Bounded linear operators on a Hilbert space H form an algebra L (H) closed for the operator norm with involution given by the adjoint operation A↦A*; it is a C*-algebra, that is, an algebra over C with a norm ∥·∥ and an involution * such that A is closed for this norm and such that ∥ab∥ ≤ …