| 1. |
- Abdeljawad, Ahmed, et al.
(författare)
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Pseudo-Differential Calculus in Anisotropic Gelfand-Shilov Setting
- 2019
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Ingår i: Integral equations and operator theory. - : Springer. - 0378-620X .- 1420-8989. ; 91:3
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Tidskriftsartikel (refereegranskat)abstract
- We study some classes of pseudo-differential operators with symbols a admitting anisotropic exponential type growth at infinity. We deduce mapping properties for these operators on Gelfand-Shilov spaces. Moreover, we deduce algebraic and certain invariance properties of these classes.
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| 2. |
- Adamyan, V., et al.
(författare)
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Dirac-Krein Systems on Star Graphs
- 2016
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Ingår i: Integral equations and operator theory. - : Springer Science and Business Media LLC. - 0378-620X .- 1420-8989. ; 86:1, s. 121-150
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Tidskriftsartikel (refereegranskat)abstract
- We study the spectrum of a self-adjoint Dirac–Krein operator with potential on a compact star graph G with a finite number n of edges. This operator is defined by a Dirac–Krein differential expression with summable matrix potentials on each edge, by self-adjoint boundary conditions at the outer vertices, and by a self-adjoint matching condition at the common central vertex of G. Special attention is paid to Robin matching conditions with parameter τ∈R∪{∞}. Choosing the decoupled operator with Dirichlet condition at the central vertex as a reference operator, we derive Krein’s resolvent formula, introduce corresponding Weyl–Titchmarsh functions, study the multiplicities, dependence on τ, and interlacing properties of the eigenvalues, and prove a trace formula. Moreover, we show that, asymptotically for R→∞, the difference of the number of eigenvalues in the intervals [0,R) and [−R,0) deviates from some integer κ0, which we call dislocation index, at most by n+2.
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| 3. |
- Albeverio, S., et al.
(författare)
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Rank one perturbations of not semibounded operators
- 1997
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Ingår i: Integral equations and operator theory. - 0378-620X .- 1420-8989. ; 27:4, s. 379-400
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Tidskriftsartikel (refereegranskat)abstract
- Rank one perturbations of selfadjoint operators which are not necessarily semibounded are studied in the present paper. It is proven that such perturbations are uniquely defined, if they are bounded in the sense of forms. We also show that form unbounded rank one perturbations can be uniquely defined if the original operator and the perturbation are homogeneous with respect to a certain one parameter semigroup. The perturbed operator is defined using the extension theory for symmetric operators. The resolvent of the perturbed operator is calculated using Krein's formula. It is proven that every rank one perturbation can be approximated in the operator norm. We prove that some form unbounded perturbations can be approximated in the strong resolvent sense without renormalization of the coupling constant only if the original operator is not semibounded. The present approach is applied to study first derivative and Dirac operators with point interaction, in one dimension
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| 4. |
- Aleman, Alexandru, et al.
(författare)
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On Ergodic Operator Means in Banach Spaces
- 2016
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Ingår i: Integral Equations and Operator Theory. - : Springer Science and Business Media LLC. - 0378-620X .- 1420-8989. ; 85:2, s. 259-287
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Tidskriftsartikel (refereegranskat)abstract
- We consider a large class of operator means and prove that a number of ergodic theorems, as well as growth estimates known for particular cases, continue to hold in the general context under fairly mild regularity conditions. The methods developed in the paper not only yield a new approach based on a general point of view, but also lead to results that are new, even in the context of the classical Cesàro means.
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| 5. |
- Andersson, Fredrik, et al.
(författare)
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On General Domain Truncated Correlation and Convolution Operators with Finite Rank
- 2015
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Ingår i: Integral Equations and Operator Theory. - : Springer Science and Business Media LLC. - 1420-8989 .- 0378-620X. ; 82:3, s. 339-370
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Tidskriftsartikel (refereegranskat)abstract
- Truncated correlation and convolution operators is a general operator-class containing popular operators such as Toeplitz (Wiener-Hopf), Hankel and finite interval convolution operators as well as small and big Hankel operators in several variables. We completely characterize the symbols for which such operators have finite rank, and develop methods for determining the rank in concrete cases. Such results are well known for the one-dimensional objects, the first discovered by L. Kronecker during the nineteenth century. We show that the results for the multidimensional case differ in various key aspects.
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| 6. |
- Betancor, Jorge J., et al.
(författare)
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UMD-Valued Square Functions Associated with Bessel Operators in Hardy and BMO Spaces
- 2015
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Ingår i: Integral equations and operator theory. - : Springer Science and Business Media LLC. - 0378-620X .- 1420-8989. ; 81:3, s. 319-374
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Tidskriftsartikel (refereegranskat)abstract
- We consider Banach valued Hardy and BMO spaces in the Bessel setting. Square functions associated with Poisson semigroups for Bessel operators are defined by using fractional derivatives. If is a UMD Banach space we obtain for -valued Hardy and BMO spaces equivalent norms involving gamma-radonifying operators and square functions. We also establish characterizations of UMD Banach spaces by means of Hardy and BMO-boundedness properties of g-functions associated to Bessel-Poisson semigroup.
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| 7. |
- Boman, Jan, et al.
(författare)
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Schrödinger Operators on Graphs and Geometry II. Spectral Estimates for L-1-potentials and an Ambartsumian Theorem
- 2018
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Ingår i: Integral equations and operator theory. - : Springer Science and Business Media LLC. - 0378-620X .- 1420-8989. ; 90:3
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we study Schrodinger operators with absolutely integrable potentials on metric graphs. Uniform bounds-i.e. depending only on the graph and the potential-on the difference between the eigenvalues of the Laplace and Schrodinger operators are obtained. This in turn allows us to prove an extension of the classical Ambartsumian Theorem which was originally proven for Schrodinger operators with Neumann conditions on an interval. We also extend a previous result relating the spectrum of a Schrodinger operator to the Euler characteristic of the underlying metric graph.
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| 8. |
- Brasche, Johannes, 1956, et al.
(författare)
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The Friedrichs extension of the Aharonov-Bohm Hamiltonian on a disc
- 2005
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Ingår i: Integral equations and operator theory. - : Springer Science and Business Media LLC. - 0378-620X .- 1420-8989. ; 52:3, s. 419-436
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Tidskriftsartikel (refereegranskat)abstract
- We show that the Aharonov-Bohm Hamiltonian considered on a disc has a four-parameter family of self-adjoint extensions. Among the infinitely many self-adjoint extensions, we determine to which parameters the Friedrichs extension H-F corresponds and its lowest eigenvalue is found. Moreover, we note that the diamagnetic inequality holds for H-F.
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| 9. |
- Brevig, Ole Fredrik, et al.
(författare)
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Weak Product Spaces of Dirichlet Series
- 2016
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Ingår i: Integral Equations and Operator Theory. - : Springer Science and Business Media LLC. - 0378-620X .- 1420-8989. ; 86:4, s. 453-473
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Tidskriftsartikel (refereegranskat)abstract
- Let (Formula presented.) denote the space of ordinary Dirichlet series with square summable coefficients, and let (Formula presented.) denote its subspace consisting of series vanishing at (Formula presented.). We investigate the weak product spaces (Formula presented.) and (Formula presented.), finding that several pertinent problems are more tractable for the latter space. This surprising phenomenon is related to the fact that (Formula presented.) does not contain the infinite-dimensional subspace of (Formula presented.) of series which lift to linear functions on the infinite polydisc. The problems considered stem from questions about the dual spaces of these weak product spaces, and are therefore naturally phrased in terms of multiplicative Hankel forms. We show that there are bounded, even Schatten class, multiplicative Hankel forms on (Formula presented.) whose analytic symbols are not in (Formula presented.). Based on this result we examine Nehari’s theorem for such Hankel forms. We define also the skew product spaces associated with (Formula presented.) and (Formula presented.), with respect to both half-plane and polydisc differentiation, the latter arising from Bohr’s point of view. In the process we supply square function characterizations of the Hardy spaces (Formula presented.), for (Formula presented.), from the viewpoints of both types of differentiation. Finally we compare the skew product spaces to the weak product spaces, leading naturally to an interesting Schur multiplier problem.
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| 10. |
- Byrnes, Christopher I., et al.
(författare)
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The generalized moment problem with complexity constraint
- 2006
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Ingår i: Integral equations and operator theory. - : Springer Science and Business Media LLC. - 0378-620X .- 1420-8989. ; 56:2, s. 163-180
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we present a synthesis of our differentiable approach to the generalized moment problem, an approach which begins with a reformulation in terms of differential forms and which ultimately ends up with a canonically derived, strictly convex optimization problem. Engineering applications typically demand a solution that is the ratio of functions in certain finite dimensional vector space of functions, usually the same vector space that is prescribed in the generalized moment problem. Solutions of this type are hinted at in the classical text by Krein and Nudelman and stated in the vast generalization of interpolation problems by Sarason. In this paper, formulated as generalized moment problems with complexity constraint, we give a complete parameterization of such solutions, in harmony with the above mentioned results and the engineering applications. While our previously announced results required some differentiability hypotheses, this paper uses a weak form involving integrability and measurability hypotheses that are more in the spirit of the classical treatment of the generalized moment problem. Because of this generality, we can extend the existence and well-posedness of solutions to this problem to nonnegative, rather than positive, initial data in the complexity constraint. This has nontrivial implications in the engineering applications of this theory. We also extend this more general result to the case where the numerator can be an arbitrary positive absolutely integrable function that determines a unique denominator in this finite-dimensional vector space. Finally, we conclude with four examples illustrating our results.
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