11 papers
The Complete Crouzeix Conjecture in Dimension Three and the Clouâtre-Ostermann-Ransford conjecture
Per Åhag, Rafał Czyż, Jani Virtanen
We settle the complete Crouzeix conjecture for matrices of order at most three and prove the Q-algebra case of the completely bounded Clouâtre--Ostermann--Ransford (COR) conjecture…
Quartic Fourier-Laplace limits for -Rogers-Szegő polynomials
Per Åhag, Rafał Czyż, Per-Håkan Lundow
We prove asymptotic formulae for -Rogers--Szegő polynomials with positive real parameters when the leading quadratic term in the logarithmic expansion about the middle coeff…
On -binomial coefficient ratios for complex parameters
Per Åhag, Rafał Czyż, Per-Håkan Lundow
We prove local asymptotics for near-central complex -binomial coefficient modulus ratios allowing an imaginary parameter perturbation of order at a len…
Maximal Plurisubharmonic Functions and Fujii-Seo Determinants in Hilbert spaces
Per Åhag, Rafał Czyż, Antti Perälä +1
A maximal plurisubharmonic function on an infinite-dimensional Hilbert space can have an injective, noncompact Levi operator at every point. This raises the question of what replac…
Continuity of Solutions to Complex Hessian Equations via the Dinew-Kołodziej Estimate
Per Åhag, Rafał Czyż
This study extends the celebrated volume-capacity estimates of Dinew and Kolodziej, providing a foundation for examining the regularity of solutions to boundary value problems for…
Generalization of Finite Entropy Measures in Kähler Geometry
P. Åhag, R. Czyż
In this paper, we extend the concept of finite entropy measures in Kähler geometry. We define the finite -entropy related to -plurisubharmonic functions and demonstrate their…
Kiselman Minimum Principle and Rooftop Envelopes in Complex Hessian Equations
Per Åhag, Rafał Czyż, Chinh H. Lu +1
We initiate the study of -subharmonic functions with respect to a semipositive -form in Euclidean domains, providing a significant element in understanding geodesics with…
Geodesic connectivity and rooftop envelopes in the Cegrell classes
Per Åhag, Rafał Czyż, Chinh H. Lu +1
This study examines geodesics and plurisubharmonic envelopes within the Cegrell classes on bounded hyperconvex domains in . We establish that solutions possessing com…
On manifold-like polyfolds as differential geometrical objects with applications in complex geometry
Per Åhag, Rafał Czyż, Håkan Samuelsson Kalm +1
We argue for more widespread use of manifold-like polyfolds (M-polyfolds) as differential geometric objects. M-polyfolds possess a distinct advantage over differentiable manifolds,…
Complex branches of a generalised Lambert function arising from --binomial coefficients
Per Åhag, Rafał Czyż, Per-Håkan Lundow
The -function, which solves the equation for , has a natural connection to the renowned Lambert function and also physical relevance through its…
Explicit Solutions in Isotropic Planar Elastostatics
Andreas Granath, Per Åhag, Antti Perälä +1
Addressing the intricate challenges in plane elasticity, especially with non-vanishing traction and complex geometries, requires innovative methods. This paper offers a novel appro…