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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
Digital watermarking is done by adding a piece of data to a signal, which depending on the target media type, may be a picture, audio or video signal. The purpose of this additional signal is to provide a consistent signature linked to the original source which then remains through the act of copying. This allows the author to obstruct the act of theft by adding this signal to his or her creation.
This work investigates crew opinions about manual intervention on board submarines and planned new solutions on the new submarine, the A26. The planned solutions include an unmanned aft and the installation of water mist instead of Halon 1301 as fire suppression system. Literature, survey and interviews were used to gather information. The crew routines and previous fire incidents were determined.
