| 1. |
- Chantraine, Baptiste, et al.
(författare)
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Doubly slice knots and obstruction to Lagrangian concordance
- 2023
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Ingår i: Comptes rendus. Mathematique. - : Cellule MathDoc/Centre Mersenne. - 1631-073X .- 1778-3569. ; 361:1, s. 1605-1609
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Tidskriftsartikel (refereegranskat)abstract
- In this short note we observe that a result of Eliashberg and Polterovitch allows to use the doubly slice genus as an obstruction for a Legendrian knot to be a slice of a Lagrangian concordance from the trivial Legendrian knot with maximal Thurston-Bennequin invariant to itself. This allows to obstruct concordances from the Pretzel knot P(3,-3,-m) when m >= 4 to the unknot. Those examples are of interest because the Legendrian contact homology algebra cannot be used to obstruct such a concordance.
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| 2. |
- El Moize, Othmane, et al.
(författare)
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A q-deformation of true-polyanalytic Bargmann transforms when q(-1) > 1
- 2021
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Ingår i: Comptes rendus. Mathematique. - : Cellule MathDoc/CEDRAM. - 1631-073X .- 1778-3569. ; 359:10, s. 1295-1305
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Tidskriftsartikel (refereegranskat)abstract
- We combine continuous q(-1)-Hermite Askey polynomials with new 2D orthogonal polynomials introduced by Ismail and Zhang as q-analogs for complex Hermite polynomials to construct a new set of coherent states depending on a nonnegative integer parameter m. Our construction leads to a new q-deformation of the m-true- polyanalytic Bargmann transform on the complex plane. In the analytic case m = 0, the obtained coherent states transform can be associated with the Arik-Coon oscillator for q(0) = q(-1) > 1. These result may be used to introduce a q-deformed Ginibre-type point process.
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| 3. |
- Johansson, B. Tomas
(författare)
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On non-denseness for a method of fundamental solutions with source points fixed in time for parabolic equations
- 2021
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Ingår i: Comptes rendus. Mathematique. - : centre Mersenne pour ldition scientifique ouverte. - 1631-073X .- 1778-3569. ; 359:6, s. 733-738
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Tidskriftsartikel (refereegranskat)abstract
- Linear combinations of fundamental solutions to the parabolic heat equation with source points fixed in Lime is investigated. The open problem whether these linear combinations generate a dense set in the space of square integrable functions on the lateral boundary of a space-time cylinder, is settled in the negative. Linear independence of the set of fundamental solutions is shown to hold. it is outlined at the end, for a particular example, that such linear combinations constitute a linearly independent and dense set in the space of square integrable functions on the upper top part (where time is fixed) of the boundary of this space-time cylinder.
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| 4. |
- Luger, Annemarie, et al.
(författare)
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On quasi-Herglotz functions in one variable : [Sur les fonctions quasi-Herglotz d’une variable]
- 2022
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Ingår i: Comptes rendus. Mathematique. - : Cellule MathDoc/CEDRAM. - 1631-073X .- 1778-3569. ; 360, s. 937-970
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, the class of (complex) quasi-Herglotz functions is introduced as the complex vector space generated by the convex cone of ordinary Herglotz functions. We prove characterization theorems, in particular, an analytic characterization. The subclasses of quasi-Herglotz functions that are identically zero in one half-plane as well as rational quasi-Herglotz functions are investigated in detail. Moreover, we relate to other areas such as weighted Hardy spaces, definitizable functions, the Cauchy transform on the unit circle, sum-rule identities and matrix-valued Herglotz functions.
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| 5. |
- Saldanha, Nicolau, et al.
(författare)
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Finiteness of rank for Grassmann convexity
- 2023
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Ingår i: Comptes rendus. Mathematique. - : Cellule MathDoc/CEDRAM. - 1631-073X .- 1778-3569. ; 361:1, s. 445-451
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Tidskriftsartikel (refereegranskat)abstract
- The Grassmann convexity conjecture, formulated in [8], gives a conjectural formula for the maximal total number of real zeroes of the consecutiveWronskians of an arbitrary fundamental solution to a disconjugate linear ordinary differential equation with real time. The conjecture can be reformulated in terms of convex curves in the nilpotent lower triangular group. The formula has already been shown to be a correct lower bound and to give a correct upper bound in several small dimensional cases. In this paper we obtain a general explicit upper bound.
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| 6. |
- Jasso, Gustavo
(författare)
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Derived equivalences of upper-triangular ring spectra via lax limits
- 2024
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Ingår i: Comptes Rendus Mathematique. - 1631-073X. ; 362, s. 279-285
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Tidskriftsartikel (refereegranskat)abstract
- We extend a theorem of Ladkani concerning derived equivalences between upper-triangular matrix rings to ring spectra. Our result also extends an analogous theorem of Maycock for differential graded algebras. We illustrate the main result with certain canonical equivalences determined by a smooth or proper ring spectrum.
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| 7. |
- Leistner, Thomas, et al.
(författare)
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Completeness of certain compact Lorentzian locally symmetric spaces
- 2023
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Ingår i: Comptes Rendus Mathematique. - 1631-073X. ; 361, s. 819-824
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Tidskriftsartikel (refereegranskat)abstract
- We show that a compact Lorentzian locally symmetric space is geodesically complete if the Lorentzian factor in the local de Rham–Wu decomposition is of Cahen–Wallach type or if the maximal flat factor is one-dimensional and time-like. Our proof uses a recent result by Mehidi and Zeghib and an earlier result by Romero and Sánchez.
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