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It is well-known that the classical Poisson kernel for the unit disc $\D$ in the complex plane is naturally associated to the Laplacian. In this paper we establish a similar relationship between the kernel $$ P_2(z)=\frac{1}{2}\frac{(1-\lvert z\rvert^2)^3}{\lvert 1-z\rvert^4}, \quad z\in\D,$$ and a certain second order differential operator $D_2(z,\partial)$. The analysis of this relationship depe
We show that a closed subspace of a dual Banach space determines boundedness if and only if it is almost norming. This result further ties up recent work on vector-valued analyticity by Arendt and Nikolski to approximation properties in the weak$^*$ topology. We also present direct proofs of two generalizations of Nelson Dunford's classical result that weak analyticity implies strong analytici
In this paper we calculate the limit of the $L^1$-means of certain weighted Poisson kernels in the unit disc and show that this limit is equal to $1$. Our result is in sharp contrast to a recent result by George F\"ulep who has shown that some related limit superiors are strictly greater than $1$. Limits of this type are of interest from the point of view of approximation theory.
Att säkerställa en effektiv konkurrens på den gemensamma marknaden är oerhört viktigt. Förbudet mot missbruk av dominerande ställning är ett av de viktigaste målen för att uppnå just detta och utgör en grundprincip. Bedömningarna i konkurrensrätten är svåra att göra eftersom varje fall är unikt och bedöms individuellt, vilket gör ämnet speciellt intressant. Då jag granskat relevant litteratur och It is crucial to ensure an effective competition on the common market. In order to do this, the prohibition against misuse of dominating position is one of the most important goals and forms a fundamental principel. What makes the subject interesting is that in competionlaw, the judgements are hard to decide as every case is unique and thus decided individually. By examining relevant literature an
This is a bachelor thesis bent on introducing the field of exoplanet research. It primarily includes descriptions of the various detection methods, with some detail into how the methods yield parameter estimates by means of least-squares algorithms. The feasibility of combining state-of-the-art astrometric capabilities of Gaia and radial velocity measurements from ground level is briefly discussed
We prove an operator identity for the shift operator in the scale of standard weighted Bergman spaces in the unit disc. This operator identity is then applied in the context of functional calculus for the shift operator and a characterization of harmonic symbol Bergman space Toeplitz operators is obtained generalizing an earlier result by Louhichi and Olofsson. Duality arguments lead to operator i
A reputation good is a good that you have to consume before you can assess its quality. Therefore, there is asymmetric information in favor of the seller. This good is also characterized by the fact that people often turn to friends and family for recommendations. On the contrary to standard economic theory of competition, an increased number of sellers on a market for reputation goods may lead to
An operator identity satisfied by the shift operator in a class of standard weighted Bergman spaces is studied. We show that subject to a pureness condition this operator identity characterizes the associated Bergman shift operator up to unitary equivalence allowing for a general multiplicity. The analysis of the general case makes contact with the class of $n$-isometries studied by Agler and Stan
The basic theory of semisimple Lie algebras and their representations is studied in detail. In particular it is shown that every irreducible module V (λ) is uniquely determined up to isomorphism by its highest weight λ. Then the problem of decomposing a tensor product of two finite dimensional modules into a direct sum of irreducible modules is considered. It is shown that for λ fixed, the decompo
Med hjälp av tredimensionella datorsimulationer har vi studerat utfallen från kollisioner mellan planeter. Målet med projektet var att utreda beroendet av kollisionsparametrar som till exempel avståndet vid närmaste passage, hastighet och planeternas massor. Vi kom fram till att planeterna kan bli gravitationellt bundna efter kollisionerna på grund av energiförluster som gör att de eventuellt kollUsing three-dimensional smoothed particle hydrodynamics (SPH) simulations, we have studied the outcomes from collisions between Jupiter-like planets. Planet models have been generated from polytropic profiles using a polytropic index of n=1 and each planet is represented by 15,000 particles. The dependency on a range of parameters specifying the point of closest approach, velocity at infinity and
In the 19th century E. Mathieu discovered and studied five multiply transitive permutation groups. The grops are called the Mathieu groups and it turned out that all five are simple. In this thesis these remarkable groups are constructed, with special focus on the largest Mathieu group M24. All maximal subgroups of M24 will be described and classied. It is also shown that the other Mathieu groups
We consider the scale of standard weighted Bergman spaces in the unit disc. We show that in this scale of spaces the shift operator satisfies a certain operator identity. By duality arguments this operator identity leads to an operator inequality for the Bergman shift operator in the parameter range $-1<\alpha\leqq0$. In the special case $\alpha=0$ the operator inequality obtained coincides with t
Sturm's oscillation theorem says that the zeros of the nth eigenfunction of a Sturm-Liouville problem with separated boundary conditions divides the domain into n connected pieces. We present a proof of this theorem which partly uses a variational characterization of the eigenfunctions. We also show how the variational characterization can be adapted to study some properties of the eigenvalues
Imaging of stellar surfaces in visible wavelengths is one of the current frontiers in astronomy. With a few exceptions, stars can not be seen in visible light as anything but point objects with current technology. Being able to properly image stars would open up the door to a vast field of new discoveries, permitting direct studies of phenomena such as rotationally deformed stars, circumstellar di
This paper consists of two parts. In the first part the following problem is presented (see [1]): a king invites n couples for dinner at his round table with 2n+1 seats. For each couple there is an in advance prescribed distance between 1 and n at which the two spouses of the couple have to be seated from each other. We show that there is a solution to the king’s problem for every choice of distan
A Poisson integral formula for a weighted Laplacian in the unit disc Beskrivning: In this paper a counterpart of the classical Poisson integral formula is found for a weighted Laplace differential operator in the unit disc. In the process the corresponding Dirichlet boundary value problem is solved for arbitrary continuous boundary data. The associated power series expansions are calculated and in
