Pomona Faculty Publications and ResearchCopyright (c) 2017 Claremont Colleges All rights reserved.
http://scholarship.claremont.edu/pomona_fac_pub
Recent documents in Pomona Faculty Publications and Researchen-usWed, 18 Jan 2017 16:07:09 PST3600Toeplitz determinants with perturbations in the corners
http://scholarship.claremont.edu/pomona_fac_pub/438
http://scholarship.claremont.edu/pomona_fac_pub/438Wed, 18 Jan 2017 15:58:35 PST
This paper is devoted to exact and asymptotic formulas for the determinants of Toeplitz matrices with perturbations by blocks of fixed size in the four corners. If the norms of the inverses of the unperturbed matrices remain bounded as the matrix dimension goes to infinity, then standard perturbation theory yields asymptotic expressions for the perturbed determinants. This premise is not satisfied for matrices generated by so-called Fisher-Hartwig symbols. In that case we establish formulas for pure single Fisher-Hartwig singularities and for the Hermitian matrices induced by general Fisher-Hartwig symbols.
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Albrecht BĂ¶ttcher et al.Permutation invariant lattices
http://scholarship.claremont.edu/pomona_fac_pub/437
http://scholarship.claremont.edu/pomona_fac_pub/437Wed, 18 Jan 2017 15:58:27 PST
We say that a Euclidean lattice in R^{n} is permutation invariant if its automorphism group has non-trivial intersection with the symmetric group S_{n}, i.e., if the lattice is closed under the action of some non-identity elements of S_{n}. Given a fixed element T E S_{n}, we study properties of the set of all lattices closed under the action of T: we call such lattices T-invariant. These lattices naturally generalize cyclic lattices introduced by Micciancio in [7,8], which we previously studied in [1].Continuing our investigation, we discuss some basic properties of permutation invariant lattices, in particular proving that the subset of well-rounded latices in the set of all T-invariant lattices in R^{n} has positive co-dimension (and hence comprises zero proportion) for all T different from an n-cycle.
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Lenny Fukshansky et al.Mathematical and physical aspects of complex symmetric operators
http://scholarship.claremont.edu/pomona_fac_pub/436
http://scholarship.claremont.edu/pomona_fac_pub/436Tue, 17 Jan 2017 11:56:27 PST
Recent advances in the theory of complex symmetric operators are presented and related to current studies in non-hermitian quantum mechanics. The main themes of the survey are: the structure of complex symmetric operators, C-selfadjoint extensions of C-symmetric unbounded operators, resolvent estimates, reality of spectrum, bases of C-orthonormal vectors, and conjugate-linear symmetric operators. The main results are complemented by a variety of natural examples arising in field theory, quantum physics, and complex variables.
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Stephan Ramon Garcia et al.An Extremal Problem for Characteristic Functions
http://scholarship.claremont.edu/pomona_fac_pub/435
http://scholarship.claremont.edu/pomona_fac_pub/435Fri, 16 Dec 2016 13:57:57 PST
Suppose E is a subset of the unit circle T and H^{infinity} C L^{infinity} is the Hardy subalgebra. We examine the problem of finding the distance from the characteristic function of E to z^{n}H^{infinity}. This admits an alternate description as a dual extremal problem. Precise solutions are given in several important cases. The techniques used involve the theory of Toeplitz and Hankel operators as well as the construction of certain conformal mappings.
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Stephan Ramon Garcia et al.Four Quotient Set Gems
http://scholarship.claremont.edu/pomona_fac_pub/434
http://scholarship.claremont.edu/pomona_fac_pub/434Fri, 16 Dec 2016 13:57:49 PST
Our aim in this note is to present four remarkable facts about quotient sets. These observations seem to have been overlooked by the MONTHLY, despite its intense coverage of quotient sets over the years.
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Stephan Ramon Garcia et al.A Non-Linear Extremal Problem on the Hardy Space
http://scholarship.claremont.edu/pomona_fac_pub/433
http://scholarship.claremont.edu/pomona_fac_pub/433Tue, 13 Dec 2016 17:05:30 PST
We relate some classical extremal problems on the Hardy space to norms of truncated Toeplitz operators and complex symmetric operators.
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Stephan Ramon Garcia et al.Inner matrices and Darlington synthesis
http://scholarship.claremont.edu/pomona_fac_pub/432
http://scholarship.claremont.edu/pomona_fac_pub/432Tue, 13 Dec 2016 17:05:25 PST
We describe and parameterize the solutions of the scalar valued Darlington synthesis problem. In the case of rational data we derive a simple procedure for producing all possible solutions.
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Stephan Ramon GarciaReview: On complex symmetric Toeplitz operators
http://scholarship.claremont.edu/pomona_fac_pub/431
http://scholarship.claremont.edu/pomona_fac_pub/431Fri, 09 Dec 2016 13:58:34 PSTStephan Ramon GarciaReview: On rank one perturbations of complex symmetric operators
http://scholarship.claremont.edu/pomona_fac_pub/430
http://scholarship.claremont.edu/pomona_fac_pub/430Fri, 09 Dec 2016 13:58:29 PSTStephan Ramon GarciaReview: A C*-algebra approach to complex symmetric operators
http://scholarship.claremont.edu/pomona_fac_pub/429
http://scholarship.claremont.edu/pomona_fac_pub/429Fri, 09 Dec 2016 13:58:24 PSTStephan Ramon GarciaReview: Transitivity and bundle shifts
http://scholarship.claremont.edu/pomona_fac_pub/428
http://scholarship.claremont.edu/pomona_fac_pub/428Fri, 09 Dec 2016 13:58:19 PSTStephan Ramon GarciaReview: A short introduction to de Branges-Rovnyak spaces
http://scholarship.claremont.edu/pomona_fac_pub/427
http://scholarship.claremont.edu/pomona_fac_pub/427Fri, 09 Dec 2016 13:58:13 PSTStephan Ramon GarciaReview: Nevanlinna-Pick spaces with hyponormal multiplication operators
http://scholarship.claremont.edu/pomona_fac_pub/426
http://scholarship.claremont.edu/pomona_fac_pub/426Fri, 09 Dec 2016 13:58:08 PSTStephan Ramon GarciaReview: On pairs of generalized and hypergeneralized projections in a Hilbert space
http://scholarship.claremont.edu/pomona_fac_pub/425
http://scholarship.claremont.edu/pomona_fac_pub/425Fri, 09 Dec 2016 13:58:03 PSTStephan Ramon GarciaReview: On symplectic self-adjointness of Hamiltonian operator matrices
http://scholarship.claremont.edu/pomona_fac_pub/424
http://scholarship.claremont.edu/pomona_fac_pub/424Fri, 09 Dec 2016 13:57:58 PSTStephan Ramon GarciaReview: Truncated Toeplitz operators of finite rank
http://scholarship.claremont.edu/pomona_fac_pub/423
http://scholarship.claremont.edu/pomona_fac_pub/423Fri, 09 Dec 2016 13:57:53 PSTStephan Ramon GarciaReview: The relationships among multiplicities of a J-self-adjoint differential operator's eigenvalue
http://scholarship.claremont.edu/pomona_fac_pub/422
http://scholarship.claremont.edu/pomona_fac_pub/422Fri, 09 Dec 2016 13:57:45 PSTStephan Ramon GarciaReview: Unitary equivalence to truncated Toeplitz operators
http://scholarship.claremont.edu/pomona_fac_pub/421
http://scholarship.claremont.edu/pomona_fac_pub/421Fri, 09 Dec 2016 13:57:39 PSTStephan Ramon GarciaIntrinsic linking and knotting are arbitrarily complex
http://scholarship.claremont.edu/pomona_fac_pub/420
http://scholarship.claremont.edu/pomona_fac_pub/420Fri, 18 Nov 2016 12:51:46 PST
We show that, given any n and alpha, any embedding of any sufficiently large complete graph in R^{3} contains an oriented link with components Q_{1},...,Q_{n} such that for every i not equal to j, Ilk(Q_{i},Q_{j})I greater than or equal to alpha and la_{2}(Q_{i})l greater than or equal to alpha, where a_{2}(Q_{i}) denotes the second coefficient of the Conway polynomial of Q_{i}.
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Erica Flapan et al.A Model of DNA Knotting and Linking
http://scholarship.claremont.edu/pomona_fac_pub/419
http://scholarship.claremont.edu/pomona_fac_pub/419Thu, 17 Nov 2016 11:21:46 PST
We present a model of how DNA knots and links are formed as a result of a single recombination event, or multiple rounds of (processive) recombination events, starting with an unknotted, unlinked, or a (2,m)-torus knot or link substrate. Given these substrates, according to our model all DNA products of a single recombination event or processive recombination fall into a single family of knots and links.
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Erica Flapan et al.