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Integral Equations and Operator Theory, ISSN 0378-620X, 12/2017, Volume 89, Issue 4, pp. 465 - 492
In this paper we present equivalence results for several types of unbounded operator functions. A generalization of the concept equivalence after extension is... 
Block operator matrices | Secondary 47A10 | Operator functions | Analysis | Equivalence after extension | Primary 47A56 | Mathematics | Spectrum | MATHEMATICS | BOUNDARY EIGENVALUE PROBLEMS | Naturvetenskap | Matematisk analys | Natural Sciences | Matematik | Mathematical Analysis
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 12/2014, Volume 278, Issue 3, pp. 987 - 994
We establish an invertibility criterion for free polynomials and free functions evaluated on some tuples of matrices. We show that if the derivative is... 
Mathematics, general | 47A56 | Secondary 14A25 | Mathematics | Primary 46L52 | MATHEMATICS | MAPS
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 8/2018, Volume 289, Issue 3, pp. 837 - 857
In 1936, Margarete C. Wolf showed that the ring of symmetric free polynomials in two or more variables is isomorphic to the ring of free polynomials in... 
Secondary 05E05 | 13A50 | Free analysis | Symmetric functions in noncommuting variables | Noncommutative invariant theory | Mathematics, general | 47A56 | Mathematics | Invariant theory | 17A50 | 47A63 | Primary 46L52 | MATHEMATICS | INVARIANTS | HOLOMORPHIC-FUNCTIONS | NONCOMMUTING VARIABLES | OPERATORS
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 12/2018, Volume 291, Issue 17-18, pp. 2590 - 2598
In the theory of orthogonal polynomials, (non‐trivial) probability measures on the unit circle are parametrized by the Verblunsky coefficients. Baxter's... 
47A56 | Baxter's theorem | Nehari problem | 42C05 | 47B35 | orthogonal polynomials | MATHEMATICS | COEFFICIENTS | PREDICTION
Journal Article
Mathematische Annalen, ISSN 0025-5831, 6/2012, Volume 353, Issue 2, pp. 519 - 522
If $${u \mapsto A(u)}$$ is a C 0,α -mapping, for 0 < α ≤ 1, having as values unbounded self-adjoint operators with compact resolvents and common domain of... 
Primary 47A55 | Mathematics, general | 47A56 | Mathematics | 47B25 | MATHEMATICS
Journal Article
Linear and Multilinear Algebra, ISSN 0308-1087, 2019, pp. 1 - 16
Journal Article
Proceedings of the London Mathematical Society, ISSN 0024-6115, 04/2019, Volume 118, Issue 4, pp. 787 - 825
The main result of this paper establishes the free analog of Grothendieck's theorem on bijective polynomial mappings of Cg. Namely, we show if p is a... 
46L52 | 47A56 | 08B20 | 47L25 (primary) | 16L30 (secondary) | MATHEMATICS | ALGEBRAS | AUTOMORPHISM | JACOBIAN CONJECTURE
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 9/2013, Volume 193, Issue 3, pp. 501 - 538
This paper resolves affirmatively Koplienko’s (Sib. Mat. Zh. 25:62–71, 1984) conjecture on existence of higher order spectral shift measures. Moreover, the... 
47A55 | 46L52 | Mathematics, general | 47A56 | Mathematics | MATHEMATICS | ALGEBRAS | DOUBLE OPERATOR INTEGRALS | SPACES | FLOW | Functions (mathematics) | Continuity | Spectra | Mathematical analysis
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 3/2017, Volume 107, Issue 3, pp. 467 - 474
Journal Article
Journal of Pure and Applied Algebra, ISSN 0022-4049, 07/2016, Volume 220, Issue 7, pp. 2533 - 2548
The matrix Fejér–Riesz theorem characterizes positive semidefinite matrix polynomials on the real line . We extend a characterization to arbitrary closed... 
47A56 | 14P10 | 13J30 | POLYNOMIALS | MATHEMATICS | MULTIDIMENSIONAL MOMENT PROBLEM | POSITIVSTELLENSATZE | MATHEMATICS, APPLIED | RINGS | SQUARES | POSITIVITY | SUMS
Journal Article
Advances in Mathematics, ISSN 0001-8708, 06/2018, Volume 331, pp. 589 - 626
The free singularity locus of a noncommutative polynomial is defined to be the sequence of hypersurfaces . The main theorem of this article shows that is... 
Linear matrix inequality | Singularity locus | Invariant theory | Noncommutative polynomial | Factorization | Spectrahedron | RATIONAL FUNCTIONS | INVARIANTS | ALGEBRAIC-GEOMETRY | CONJECTURE | MATHEMATICS | SYSTEMS | PENCILS | DOMAINS
Journal Article
Integral Equations and Operator Theory, ISSN 0378-620X, 8/2018, Volume 90, Issue 4, pp. 1 - 30
Let S be a symmetric operator with finite and equal defect numbers in the Hilbert space $${{\mathfrak {H}}}$$ H . We study the compressions $$P_{{\mathfrak... 
Compression | Symmetric and self-adjoint operators | 47B25 | Analysis | Krein’s resolvent formula | Q -function | Self-adjoint extension | 47A56 | Mathematics | Hilbert space | 47A20 | Generalized resolvent | Q-function
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 09/2018, Volume 291, Issue 13, pp. 1941 - 1978
The present part of the paper develops a geometrical approach to the study of factorizations of contractive operator functions in the class L∞. The proposed... 
Secondary: 47A20 | regular factorization | 47A57 | contractive operator function | factorizing channel of a unitary coupling | Primary: 47A56 | 47A40 | scattering suboperator | MATHEMATICS
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 07/2019, Volume 371, Issue 7, pp. 4837 - 4868
Journal Article
Monatshefte für Mathematik, ISSN 0026-9255, 12/2019, Volume 190, Issue 4, pp. 599 - 614
It is known that any harmonic map of finite uniton number from a Riemann surface into $$\mathrm {U}(n)$$ U ( n ) can be deformed into a new harmonic map with... 
Blaschke–Potapov products | Unitons | 58E20 | Shift-invariant subspaces | Mathematics, general | 47A56 | Mathematics | Bruhat decomposition | Harmonic maps | Extended solutions | Naturvetenskap | Natural Sciences | Matematik
Journal Article
Integral Equations and Operator Theory, ISSN 0378-620X, 2/2019, Volume 91, Issue 1, pp. 1 - 55
The goal of this paper is to study the Bohr phenomenon in the setting of free holomorphic functions on noncommutative regular polydomains $$\mathbf{D_f^m}$$... 
Noncommutative polydomain | 46L52 | Bohr’s inequality | Weighted Fock space | Analysis | Primary 47A56 | Secondary 32A38 | Free holomorphic function | Berezin transform | Mathematics | Multivariable operator theory | 47A63 | MATHEMATICS | RADIUS | Bohr's inequality | THEOREM | TRANSFORMS
Journal Article
Integral Equations and Operator Theory, ISSN 0378-620X, 4/2019, Volume 91, Issue 2, pp. 1 - 27
Let A be a symmetric linear relation in the Hilbert space $${\mathfrak {H}}$$ H with equal deficiency indices $$n_\pm (A)\le \infty $$ n±(A)≤∞ . A self-adjoint... 
Exit space self-adjoint extension | Compression | 47A06 | Symmetric and self-adjoint linear relation (operator) | 47B25 | Analysis | 47A56 | Mathematics | 47A20 | Boundary triplet | MATHEMATICS | GENERALIZED RESOLVENTS | BOUNDARY RELATIONS | OPERATORS | Numerical analysis
Journal Article
Numerische Mathematik, ISSN 0029-599X, 2014, Volume 126, Issue 3, p. 413
Galerkin spectral approximation theory for non-self-adjoint quadratic operator polynomials with periodic coefficients is considered. The main applications are... 
Naturvetenskap | Computational Mathematics | 65F15 | 47A56 | Mathematics | 65M60 | Natural Sciences | Beräkningsmatematik | Matematik | 35P30
Journal Article
Complex Analysis and Operator Theory, ISSN 1661-8254, 4/2019, Volume 13, Issue 3, pp. 1133 - 1141
In this paper, using the notion of superquadratic functions and operator valued mappings, we give an improvement of the Hardy inequality for Hilbert space... 
Secondary 47A56 | Operator Theory | Analysis | Mathematics, general | Hardy inequality | Superquadratic function | Mathematics | Weakly measurable mapping | Primary 26D15 | p -integrable | p-integrable
Journal Article
Integral Equations and Operator Theory, ISSN 0378-620X, 1/2014, Volume 78, Issue 1, pp. 71 - 73
If A and B are contraction operators on a Hilbert space $${\mathcal{H}}$$ H that commute with a shift operator S, it is shown that A = BC for some contraction... 
Secondary 47A45 | analytic operator | Leech’s theorem | Analysis | 47A68 | Primary 47A56 | contraction | Mathematics | Shift operator | factorization | 47A63 | Leech's theorem | MATHEMATICS
Journal Article
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