Lax-phillips Scattering and Conservative Linear Systems: A Cuntz-algebra Multidimensional Setting

By Joseph A. Ball, Victor Vinnikov. 2005

78 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/d0f974397ae47d230d2fb866329f57f8e3016553

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In Mathematical Physics

Citations in the corpus

Foundations of Free Noncommutative Function Theory (2012, background): “These systems were first studied in [20] in the conservative infinite-dimensional setting, in the context of operator model theory for row contractions due mostly to Popescu [81, 82, 83, 84] and of representation theory of the Cuntz algebra [27, 32].”
Operator Theory on Noncommutative Domains (2007, unknown): “The model theory for row contractions (elements of [B(H)]1) (see [66], [67], and [68]) lead Ball and Vinikov [17] to their multivariable setting for Lax-Phillips scattering and conservative linear systems.”
Free holomorphic functions on the unit ball of B(H)n (2006, unknown): “) and its applications concerning interpolation in several variables ([27], [31], [33], [3], [15], [6], [37], etc.) and unitary invariants for n-tuples of operators ([27], [4], [5], [35], [21], [36], [7], [37], [40], etc.). Our program to develop a free analogue of Sz.-Nagy–Foia¸s theory [50], for r”
Free holomorphic functions and interpolation (2007, background): “In the last two decades, significant progress has been made in noncommutative multivariable operator theory regarding noncommutative dilation theory and its applications to interpolation in several variables ([24], [28], [40], [38], [30], [4], [36]), and unitary invariants for n-tuples of operators ”
Noncommutative reproducing kernel Hilbert spaces (2016, background): “5 makes the identification between the notion of formal reproducing kernel Hilbert space introduced earlier by two of the present authors in [14] (see also [15]) and a noncommutative reproducing kernel Hilbert space introduced here.”