| 1. |
- Ameur, Yacin, et al.
(författare)
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On boundary confinements for the Coulomb gas
- 2020
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Ingår i: Analysis and Mathematical Physics. - : Springer Science and Business Media LLC. - 1664-2368 .- 1664-235X. ; 10:4
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Tidskriftsartikel (refereegranskat)abstract
- We introduce a family of boundary confinements for Coulomb gas ensembles, and study them in the two-dimensional determinantal case of random normal matrices. The family interpolates between the free boundary and hard edge cases, which have been well studied in various random matrix theories. The confinement can also be relaxed beyond the free boundary to produce ensembles with fuzzier boundaries, i.e., where the particles are more and more likely to be found outside of the boundary. The resulting ensembles are investigated with respect to scaling limits and distribution of the maximum modulus. In particular, we prove existence of a new point field—a limit of scaling limits to the ultraweak point when the droplet ceases to be well defined.
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| 2. |
- Andersson, Jonathan, et al.
(författare)
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Effect of density dependence on coinfection dynamics
- 2021
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Ingår i: Analysis and Mathematical Physics. - Basel, Switzerland : Birkhaeuser Science. - 1664-2368 .- 1664-235X. ; 11:4
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we develop a compartmental model of SIR type (the abbreviation refers to the number of Susceptible, Infected and Recovered people) that models the population dynamics of two diseases that can coinfect. We discuss how the underlying dynamics depends on the carrying capacity K: from a simple dynamics to a more complex. This can also help in understanding the appearance of more complicated dynamics, for example, chaos and periodic oscillations, for large values of K. It is also presented that pathogens can invade in population and their invasion depends on the carrying capacity K which shows that the progression of disease in population depends on carrying capacity. More specifically, we establish all possible scenarios (the so-called transition diagrams) describing an evolution of an (always unique) locally stable equilibrium state (with only non-negative compartments) for fixed fundamental parameters (density independent transmission and vital rates) as a function of the carrying capacity K. An important implication of our results is the following important observation. Note that one can regard the value of K as the natural ‘size’ (the capacity) of a habitat. From this point of view, an isolation of individuals (the strategy which showed its efficiency for COVID-19 in various countries) into smaller resp. larger groups can be modelled by smaller resp. bigger values of K. Then we conclude that the infection dynamics becomes more complex for larger groups, as it fairly maybe expected for values of the reproduction number R0≈1. We show even more, that for the values R0>1 there are several (in fact four different) distinguished scenarios where the infection complexity (the number of nonzero infected classes) arises with growing K. Our approach is based on a bifurcation analysis which allows to generalize considerably the previous Lotka-Volterra model considered previously in Ghersheen et al. (Math Meth Appl Sci 42(8), 2019).
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| 3. |
- Andersson, Jonathan, et al.
(författare)
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Effect of density dependence on coinfection dynamics : part 2
- 2021
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Ingår i: Analysis and Mathematical Physics. - : Springer Basel AG. - 1664-2368 .- 1664-235X. ; 11:4
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we continue the stability analysis of the model for coinfection with density dependent susceptible population introduced in Andersson et al. (Effect of density dependence on coinfection dynamics. arXiv:2008.09987, 2020). We consider the remaining parameter values left out from Andersson et al. (Effect of density dependence on coinfection dynamics. arXiv:2008.09987, 2020). We look for coexistence equilibrium points, their stability and dependence on the carrying capacity K. Two sets of parameter value are determined, each giving rise to different scenarios for the equilibrium branch parametrized by K. In both scenarios the branch includes coexistence points implying that both coinfection and single infection of both diseases can exist together in a stable state. There are no simple explicit expression for these equilibrium points and we will require a more delicate analysis of these points with a new bifurcation technique adapted to such epidemic related problems. The first scenario is described by the branch of stable equilibrium points which includes a continuum of coexistence points starting at a bifurcation equilibrium point with zero single infection strain #1 and finishing at another bifurcation point with zero single infection strain #2. In the second scenario the branch also includes a section of coexistence equilibrium points with the same type of starting point but the branch stays inside the positive cone after this. The coexistence equilibrium points are stable at the start of the section. It stays stable as long as the product of K and the rate γ¯γ¯ of coinfection resulting from two single infections is small but, after this it can reach a Hopf bifurcation and periodic orbits will appear.
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| 4. |
- Avdonin, Sergey, et al.
(författare)
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Stability estimate for an inverse problem in glaciology
- 2012
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Ingår i: Analysis and Mathematical Physics. - Basel : Birkhäuser Verlag. - 1664-2368 .- 1664-235X. ; 2:4, s. 367-387
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Tidskriftsartikel (refereegranskat)abstract
- We consider the problem of reconstruction of the basal velocity of a glacier by measurements of the velocity on glacier’s surface. The main result is a stability estimate in a near-surface region, which represents a multiplicative inequality and shows that small errors in measurements produce small errors in the velocity in this region.
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| 5. |
- Bell, Steven R., et al.
(författare)
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Ruminations on Hejhal's theorem about the Bergman and Szego kernels
- 2022
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Ingår i: Analysis and Mathematical Physics. - : Springer Nature. - 1664-2368 .- 1664-235X. ; 12:1
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Tidskriftsartikel (refereegranskat)abstract
- We give a new proof of Dennis Hejhal's theorem on the nondegeneracy of the matrix that appears in the identity relating the Bergman and Szego kernels of a smoothly bounded finitely connected domain in the plane. Mergelyan's theorem is at the heart of the argument. We explore connections of Hejhal's theorem to properties of the zeroes of the Szego kernel and propose some ideas to better understand Hejhal's original theorem.
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| 6. |
- Bénéteau, Catherine, et al.
(författare)
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On the concept of inner function in Hardy and Bergman spaces in multiply connected domains
- 2019
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Ingår i: Analysis and Mathematical Physics. - : Springer Science and Business Media LLC. - 1664-2368 .- 1664-235X. ; 9:2, s. 839-866
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Tidskriftsartikel (refereegranskat)abstract
- We discuss the notion of an inner function for spaces of analytic functions in multiply connected domains in C, giving a historical overview and comparing several possible definitions. We explore connections between inner functions, zero-divisors for Hardy spaces and Bergman spaces, and weighted reproducing kernels. After recording some obstructions and negative results, we suggest avenues for further research and point out several open problems.
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| 7. |
- Bergfeldt, Aksel, et al.
(författare)
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On weighted norm inequalities for oscillatory integral operators
- 2022
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Ingår i: Analysis and Mathematical Physics. - : Springer Science and Business Media LLC. - 1664-2368 .- 1664-235X. ; 12:6
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Tidskriftsartikel (refereegranskat)abstract
- We prove weighted norm inequalities with Muckenhoupt’s Ap-weights, for a wide class of oscillatory integral operators. As a consequence, one also obtains the boundedness of commutators of the aforementioned operators with functions in BMO.
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| 8. |
- Bergqvist, Linus
(författare)
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A note on cyclic polynomials in polydiscs
- 2018
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Ingår i: Analysis and Mathematical Physics. - : Springer Science and Business Media LLC. - 1664-2368 .- 1664-235X. ; 8:2, s. 197-211
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Tidskriftsartikel (refereegranskat)abstract
- We use methods from potential theory and harmonic analysis to show non-cyclicity of polynomials on a polydisc whose zero set meets the distinguished boundary along a hypersurface. We also generalize methods used for proving cyclicity for polynomials in two variables with small zero sets to arbitrary dimension. In doing so, we show that in higher dimension, the cyclicity properties of a function do not only depend on the codimension, but also on the orientation of the zero set. Furthermore, we illustrate our results by studying a special class of polynomials. Finally, we use methods from potential theory to prove that our estimates for non-cyclicity are in fact sharp.
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| 9. |
- Bertola, Marco, et al.
(författare)
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Diagonalization of the finite Hilbert transform on two adjacent intervals : the Riemann-Hilbert approach
- 2020
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Ingår i: Analysis and Mathematical Physics. - : Springer Nature. - 1664-2368 .- 1664-235X. ; 10:3
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we study the spectra of bounded self-adjoint linear operators that are related to finite Hilbert transforms H-L : L-2([b(L), 0]) -> L-2([0, b(R)]) and H-R : L-2([0, b(R)]) -> L-2([b(L), 0]). These operators arise when one studies the interior problem of tomography. The diagonalization of H-R, H-L has been previously obtained, but only asymptotically when b(L) not equal -b(R). We implement a novel approach based on the method of matrix Riemann-Hilbert problems (RHP) which diagonalizes H-R, H-L explicitly. We also find the asymptotics of the solution to a related RHP and obtain error estimates.
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| 10. |
- Castro, Alejandro J., et al.
(författare)
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Regularity of Fourier integral operators with amplitudes in general Hormander classes
- 2021
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Ingår i: Analysis and Mathematical Physics. - : Springer Nature. - 1664-2368 .- 1664-235X. ; 11:3
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Tidskriftsartikel (refereegranskat)abstract
- We prove the global Lp-boundedness of Fourier integral operators that model the parametrices for hyperbolic partial differential equations, with amplitudes in classical Hormander classes S rho,delta m(Rn) for parameters 0 <= rho <= 1, 0 <= delta <1. We also consider the regularity of operators with amplitudes in the exotic class S0,m(Rn), 0 <= delta <1 and the forbidden class S,1m(Rn), 0 <= rho <= 1. Furthermore we show that despite the failure of the L2-boundedness of operators with amplitudes in the forbidden class S1,10(Rn), the operators in question are bounded on Sobolev spaces Hs(Rn) with s>0. This result extends those of Y. Meyer and E. M. Stein to the setting of Fourier integral operators.
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