| 1. |
- Wikström, Frank
(författare)
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The Dirichlet problem for maximal plurisubharmonic functions on analytic varieties in C^n
- 2009
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Ingår i: International Journal of Mathematics. - 0129-167X. ; 20:4, s. 521-528
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Tidskriftsartikel (refereegranskat)abstract
- Let Ω be a B-regular domain in ℂn and let V be a locally irreducible analytic variety in Ω. Given a continuous function , we prove that there is a unique maximal plurisubharmonic function u on V with boundary values given by ϕ and furthermore that u is continuous on .
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| 2. |
- Wikström, Frank
(författare)
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Funktionsteori
- 2014
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- Lärobok i grundläggande komplex analys (och serier), i första hand avsedd för civilingenjörsutbildningar. Boken är lättläst, utan att göra avkall på den matematiska noggrannheten och stringensen. För många studenter är kursen i funktionsteori det första mötet med modern matematisk analys, boken är skriven på ett sådant sätt att läsaren får så mycket hjälp som möjligt att gradvis vänja sig vid det kortfattade, barskrapade skrivsätt som brukar användas för ''högre matematik''.
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| 3. |
- Daghighi, Abtin, et al.
(författare)
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A pure smoothness condition for Radó’s theorem for α-analytic functions
- 2016
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Ingår i: Czechoslovak Mathematical Journal. - : Institute of Mathematics, Czech Academy of Sciences. - 0011-4642 .- 1572-9141. ; 66:1, s. 57-62
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Tidskriftsartikel (refereegranskat)abstract
- Let (Formula presented.) be a bounded, simply connected ℂ-convex domain. Let α ∈ ℤ+ n and let f be a function on Ω which is separately (Formula presented.) -smooth with respect to zj (by which we mean jointly (Formula presented.) -smooth with respect to Rezj, Imzj). If f is α-analytic on Ω\f−1(0), then f is α-analytic on Ω. The result is well-known for the case αi = 1, 1 ⩽ i ⩽ n, even when f a priori is only known to be continuous.
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| 4. |
- Nilsson, Mårten, et al.
(författare)
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Quasibounded plurisubharmonic functions
- 2021
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Ingår i: International Journal of Mathematics. - 0129-167X. ; 32:9
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Tidskriftsartikel (refereegranskat)abstract
- We extend the notion of quasibounded harmonic functions to the plurisubharmonic setting. As an application, using the theory of Jensen measures, we show that certain generalized Dirichlet problems with unbounded boundary data admit unique solutions, and that these solutions are continuous outside a pluripolar set.
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| 5. |
- Wikström, Frank, et al.
(författare)
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Level Sets of Certain Subclasses of α-analytic Functions
- 2017
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Ingår i: Journal of partial differential equations. - : Global Science Press. - 1000-940X. ; 30:4, s. 281-298
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Tidskriftsartikel (refereegranskat)abstract
- For an open set V subset of C-n, denote by M-alpha(V) the family of a-analytic functions that obey a boundary maximum modulus principle. We prove that, on a bounded "harmonically fat" domain Omega subset of C-n, a function f is an element of M-alpha (Omega\f(-1)(0)) automatically satisfies f is an element of M-alpha(Omega), if it is C alpha j-1-smooth in the z(j) variable, alpha is an element of Z(+)(n) up to the boundary. For a submanifold U subset of C-n, denote by M-alpha(U), the set of functions locally approximable by a-analytic functions where each approximating member and its reciprocal (off the singularities) obey the boundary maximum modulus principle. We prove, that for a C-3-smooth hypersurface, Omega, a member of M-alpha(Omega), cannot have constant modulus near a point where the Levi form has a positive eigenvalue, unless it is there the trace of a polyanalytic function of a simple form. The result can be partially generalized to C-4-smooth submanifolds of higher codimension, at least near points with a Levi cone condition.
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| 6. |
- Lind, Andreas, 1979-
(författare)
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Holomorphic automorphisms of Danielewski surfaces
- 2009
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis we define the notion of an overshear on a Danielewskisurface. Next we show that the group generated by the overshears is dense in the component of the identity of the automorphism group. Moreover, we show that the overshear group has a structure of an amalgamated product, and as consequence of this the overshear group is a proper subgroup of the automorphism group. Finally we classify the R^n-actions, and therefore the one parameter subgroups, of the overshear group. We also show that any Lie subgroup of an amalgamated product can be conjugated to one of the factors of the amalgamated product.
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