The Schur algorithm, reproducing kernel spaces and system theory

By Steve Abbott. Mathematical Gazette, 2002

116 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/83b257f707ee207d8dc2e6655a6654fd7c1fbf22

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Citations in the corpus

Schur Functions and Their Realizations in the Slice Hyperholomorphic Setting (2011, methodology): “We note (see for instance [50, 2]): Theorem 5.”
Dimensionality Reduction for Supervised Learning with Reproducing Kernel Hilbert Spaces (2004, background): “13 in Alpay (2001). From this proposition, it is obvious that EY |X [g(Y ) | X = ·] ∈ H1 holds, if the range of X and Y are bounded.”
Learning with non-positive kernels (2004, background): “K ) is a Reproducing Kernel Kre˘ın Space (Alpay, 2001, Chapter 7) if K ⊂ R X and the evaluation functional is continuous on K endowed with its strong topology (that is, via K ).”
Entire slice regular functions (2015, background): “ works of Schur, Herglotz, and others and can be seen as a collection of topics pertaining to Schur functions and their generalizations; for a quick introduction in the classical case see for example [5]. For the slice hyperholomorphic case see [1, 2, 6, 7, 12, 13, 14, 15, 16, 17, 19, 20] and also t”
The spectral theorem for quaternionic unbounded normal operators based on the S-spectrum (2014, unknown): “We point out that the S-resolvent operators are also used in Schur analysis in the realization of Schur functions in the slice hyperholomorphic setting see [1, 8, 9, 10] and [3, 11] for the classical case.”
The Spectral Theorem for Unitary Operators Based on the S-Spectrum (2014, unknown): “l calculus, see [15, 16, 17]. We point out that the S-resolvent operators are also used in Schur analysis in the realization of Schur functions in the slice hyperholomorphic setting see [6, 7, 8] and [2, 10] for the classical case. To set the framework in which we will work, we give some preliminari”
Spectral Theory for Gaussian Processes: Reproducing Kernels, Boundaries, and L2-Wavelet Generators with Fractional Scales (2015, methodology): “For reproducing kernel Hilbert spaces, see, for example, [2, 45].”
The Analytic Theory of Matrix Orthogonal Polynomials (2007, unknown): “13”
A New Resolvent Equation for the $$S$$S-Functional Calculus (2013, methodology): “The reader is referred to [2–4] for Schur analysis in the slice hyperholomorphic setting and to [1,7] for an overview of Schur analysis in the complex setting.”
Pontryagin-de Branges-Rovnyak spaces of slice hyperholomorphic functions (2012, unknown): “The equivalence between (1) and (2) follows as in [1] Theorem 2.”