Ex aliis paleas, ex istis collige grana.
"Gargantua and Pantagruel, Complete." by Francois Rabelais
I've jest called round at your lodgin's, and they towld me as you was at the Collige.
"Born in Exile" by George Gissing
I took him from collige sum 16 years ago and gave him a good situation as the Bearded Woman in my Show.
"The Complete Works of Artemus Ward" by Charles Farrar Browne (AKA Artemus Ward)
Ex aliis paleas, ex istis collige grana.
"Gargantua and Pantagruel, Book III." by Francois Rabelais
Now, so far as the particular sciences are concerned, I presume that no one will deny the supreme power of these colligating ideas.
"Browning as a Philosophical and Religious Teacher" by Henry Jones
Not only is it internally consistent, which cannot be affirmed of the reformation theory, but it colligates the facts far better.
"Kinship Organisations and Group Marriage in Australia" by Northcote W. Thomas
No other hypothesis 'colligates the facts.
"Historical Mysteries" by Andrew Lang
By November he had discovered and colligated a multitude of the most wonderful and unexpected phenomena.
"Fragments of science, V. 1-2" by John Tyndall
Dey tells me he was a collige boy, or in de army or somethin'.
"Traffic in Souls" by Eustace Hale Ball
But colligation simply sums up the facts observed, as seen under a new point of view.
"Analysis of Mr. Mill's System of Logic" by William Stebbing
His version 'colligates' them; though extravagant they become not incoherent.
"James VI and the Gowrie Mystery" by Andrew Lang
Colligation is not always induction; but induction is always colligation.
"A System of Logic: Ratiocinative and Inductive" by John Stuart Mill
The Colligation of Facts is no other than this preliminary operation.
"A System of Logic: Ratiocinative and Inductive" by John Stuart Mill
Or, in other words, they are only cognoscible as a colligation of incongruous coalescences.
"The Travelling Companions" by F. Anstey
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Realization theory for operator colligations on Pontryagin spaces is used to study interpolation and factorization in generalized Schur classes.
A note on interpolation in the generalized Schur class
Our approach is based on the use of characteristic functions of partially isometric operator colligations, and the interpolation and factorization criteria that we obtain are dictated by what is needed to construct the colligations. A scalar example gives an idea of the nature of the conditions.
A note on interpolation in the generalized Schur class
The proof uses a different colligation from that of Theorem 2.1.
A note on interpolation in the generalized Schur class
Kre˘ın) pertaining to this problem. A key step involves another application of the characteristic function of a partially isometric operator colligation, which was the principal tool in Section 2.
A note on interpolation in the generalized Schur class
The principle difference between Ambrozie’s approach and that of Agler and McCarthy then comes down to whether one views the kernel Γ as an element of a predual (Agler and McCarthy), or as an element of a dual space, along with the introduction of a more general notion of unitary colligation (Ambrozie).
Test Functions, Kernels, Realizations and Interpolation
Cb (Ψ)-unitary colligations, transfer functions, and the class F.
Test Functions, Kernels, Realizations and Interpolation
For a collection of test functions Ψ, following , deﬁne a Cb (Ψ)-unitary colligation Σ to be a tuple Σ = (U, E , ρ), E a Hilbert space, U unitary on E ⊕ C, and ρ : Cb (Ψ) → B (E ) a unital ∗-representation.
Test Functions, Kernels, Realizations and Interpolation
Let Σ = (U, E , ρ) be a Cb (Ψ)-unitary colligation with associated transfer function WΣ .
Test Functions, Kernels, Realizations and Interpolation
With the exception of (iv) in Theorem 2.2 and the concrete form of the space E for the unitary colligation in Theorem 2.3, they are in fact special cases of results to be found in .
Test Functions, Kernels, Realizations and Interpolation
Remark 2.4. (In the last theorem the representation ρ in the deﬁnition of Ψ-unitary colligation is simply a multiple of the representation of C (Ψ) as multiplication operators on L2 (µ).
Test Functions, Kernels, Realizations and Interpolation
U, E , ρ) is a Cb (Ψ)-unitary colligation; (ii) the representation ρ is simple; (iii) π ∈ F; and (iv) ϕ = D + C Z (I − AZ )−1B , where Z = ρ(E ), then π(ϕ) is a contraction.
Test Functions, Kernels, Realizations and Interpolation
Products of Nevanlinna-Pick kernels and operator colligations.
Test Functions, Kernels, Realizations and Interpolation
D if and only if there is a unitary colligation matrix U = C D ] : X ⊕ U → X ⊕ Y so that S (z ) = D + zC (I − zA)−1B .
Test functions, Schur-Agler classes and transfer-function realizations: the matrix-valued setting
Section 2 presents some preliminary material on test functions, positive kernels, and structured unitary colligation matrices needed in the sequel.
Test functions, Schur-Agler classes and transfer-function realizations: the matrix-valued setting
In the test function approach to interpolation and commutant lifting, those functions built from the test functions as a transfer function of a unitary colligation play a key role and are known as Agler-Schur class functions.
Agler-Commutant Lifting on an Annulus
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