| 1. |
- O'Farrell, Anthony G, et al.
(författare)
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Conjugacy of real diffeomorphisms. A survey.
- 2011
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Ingår i: St. Peterburg Mathematical Journal. - 1547-7371 .- 1061-0022. ; 22, s. 1-40
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Tidskriftsartikel (refereegranskat)abstract
- Given a group G, the conjugacy problem in G is the problem of giving an effective procedure for determining whether or not two given elements f, g of G are conjugate, i.e. whether there exists h belonging to G with fh = hg. This paper is about the conjugacy problem in the group Diffeo(I) of all diffeomorphisms of an interval I in R. There is much classical work on the subject, solving the conjugacy problem for special classes of maps. Unfortunately, it is also true that many results and arguments known to the experts are difficult to find in the literature, or simply absent. We try to repair these lacunae, by giving a systematic review, and we also include new results about the conjugacy classification in the general case.
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| 2. |
- Rozenblioum, Grigori, 1948, et al.
(författare)
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On Spectral Estimates for the Schrodinger Operators in Global Dimension 2
- 2014
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Ingår i: St Petersburg Mathematical Journal. - 1061-0022 .- 1547-7371. ; 25:3, s. 495-505
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Tidskriftsartikel (refereegranskat)abstract
- The problem of finding eigenvalue estimates for the Schrodinger operator turns out to be most complicated for the dimension 2. Some important results for this case have been obtained recently. In the paper, these results are discussed, and their counterparts are established for the operator on the combinatorial and metric graphs corresponding to the lattice Z(2).
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| 3. |
- Asekritova, Irina, et al.
(författare)
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Interpolation of Besov spaces in the nondiagonal case
- 2006
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Ingår i: St. Petersburg Mathematical Journal. - 1061-0022 .- 1547-7371. ; 18:4, s. 1-9
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Tidskriftsartikel (refereegranskat)abstract
- In the nondiagonal case, interpolation spaces for a collection of Besov spaces are described. The results are consequences of the fact that, whenever the convex hull of points (formula presented) includes a ball of ℝm+1, we have (formula presented).
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| 4. |
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| 5. |
- Apushkinskaya, D. E., et al.
(författare)
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Lipschitz property of the free boundary in the parabolic obstacle problem
- 2004
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Ingår i: St. Petersburg Mathematical Journal. - 1061-0022 .- 1547-7371. ; 15:3, s. 375-391
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Tidskriftsartikel (refereegranskat)abstract
- A parabolic obstacle problem with zero constraint is considered. It is proved, without any additional assumptions on a free boundary, that near the fixed boundary where the homogeneous Dirichlet condition is fulfilled, the boundary of the noncoincidence set is the graph of a Lipschitz function.
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| 6. |
- Baranov, A., et al.
(författare)
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Subspaces of de branges spaces with prescribed growth
- 2007
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Ingår i: St. Petersburg Mathematical Journal. - 1061-0022 .- 1547-7371. ; 18:5, s. 699-716
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Tidskriftsartikel (refereegranskat)abstract
- The growth properties of de Branges spaces and their subspaces are studied. It is shown that, for each given pair of growth functions λ(r) = O(r) and λ1 = o(λ), there exist de Branges spaces of growth λ that have a de Branges subspace of growth λ1. This phenomenon cannot occur for a class of de Branges spaces that, in a certain sense, behave regularly along the real axis.
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| 7. |
- Kozlov, Vladimir, et al.
(författare)
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The spectrum asymptotics for the Dirichlet problem in the case of the biharmonic operator in a domain with highly indented boundary
- 2011
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Ingår i: St. Petersburg Mathematical Journal. - 1061-0022 .- 1547-7371. ; 22:6, s. 941-983
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Tidskriftsartikel (refereegranskat)abstract
- Asymptotic expansions are constructed for the eigenvalues of the Dirichlet problem for the biharmonic operator in a domain with highly indented and rapidly oscillating boundary (the Kirchhoff model of a thin plate). The asymptotic constructions depend heavily on the quantity γ that describes the depth O(εγ) of irregularity (ε is the oscillation period). The resulting formulas relate the eigenvalues in domains with close irregular boundaries and make it possible, in particular, to control the order of perturbation and to find conditions ensuring the validity (or violation) of the classical Hadamard formula.
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| 8. |
- Shimorin, Serguei
(författare)
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Branching points area theorems for univalent functions
- 2007
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Ingår i: St. Petersburg Mathematical Journal. - 1061-0022 .- 1547-7371. ; 18:1, s. 141-181
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Tidskriftsartikel (refereegranskat)abstract
- Area theorems of a new type are obtained by considering branching point compositions with univalent functions. Such theorems can be formulated both in the form of integral estimates and in the form of Grunsky and Goluzin-type inequalities.
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| 9. |
- Olofsson, Anders
(författare)
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Operator-valued Bergman inner functions as transfer functions
- 2008
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Ingår i: St. Petersburg Mathematical Journal. - 1061-0022. ; 19:4, s. 603-623
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Tidskriftsartikel (refereegranskat)abstract
- An explicit construction characterizing the operator-valued Bergman inner functions is given for a class of vector-valued standard weighted Bergman spaces in the unit disk. These operator-valued Bergman inner functions act as contractive multipliers from the Hardy space into the associated Bergman space, and they have a natural interpretation as transfer functions for a related class of discrete time linear systems. This points to a new interaction between the fields of invariant subspace theory and mathematical systems theory.
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| 10. |
- Shah gholian, Henrik
(författare)
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REGULARITY ISSUES FOR SEMILINEAR PDE-S (A NARRATIVE APPROACH)
- 2016
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Ingår i: St. Petersburg Mathematical Journal. - : American Mathematical Society (AMS). - 1061-0022 .- 1547-7371. ; 27:3, s. 577-587
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Tidskriftsartikel (refereegranskat)abstract
- Occasionally, solutions of semilinear equations have better (local) regularity properties than the linear ones if the equation is independent of space (and time) variables. The simplest example, treated by the current author, was that the solutions of Delta u = f(u), with the mere assumption that f ' >= -C, have bounded second derivatives. In this paper, some aspects of semilinear problems are discussed, with the hope to provoke a study of this type of problems from an optimal regularity point of view. It is noteworthy that the above result has so far been undisclosed for linear second order operators, with Holder coefficients. Also, the regularity of level sets of solutions as well as related quasilinear problems are discussed. Several seemingly plausible open problems that might be worthwhile are proposed.
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