| 1. |
- Andersson, Anders
(author)
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On the curvature of an inner curve in a Schwarz-Christoffel mapping
- 2007
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Reports (other academic/artistic)abstract
- In the so called outer polygon method, an approximative conformal mapping for a given simply connected region \Omega is constructed using a Schwarz-Christoffel mapping for an outer polygon, a polygonal region of which \Omega is a subset. The resulting region is then bounded by a C^\infty -curve, which among other things means that its curvature is bounded. In this work, we study the curvature of an inner curve in a polygon, i.e., the image under the Schwarz-Christoffel mapping from R, the unit disk or upper halfplane, to a polygonal region P of a curve inside R. From the Schwarz-Christoffel formula, explicit expressions for the curvature are derived, and for boundary curves, appearing in the outer polygon method, estimations of boundaries for the curvature are given.
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| 3. |
- Araaya, Tsehaye, 1962-
(author)
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The Symmetric Meixner-Pollaczek polynomials
- 2003
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Doctoral thesis (other academic/artistic)abstract
- The Symmetric Meixner-Pollaczek polynomials are considered. We denote these polynomials in this thesis by pn(λ)(x) instead of the standard notation pn(λ) (x/2, π/2), where λ > 0. The limiting case of these sequences of polynomials pn(0) (x) =limλ→0 pn(λ)(x), is obtained, and is shown to be an orthogonal sequence in the strip, S = {z ∈ ℂ : −1≤ℭ (z)≤1}.From the point of view of Umbral Calculus, this sequence has a special property that makes it unique in the Symmetric Meixner-Pollaczek class of polynomials: it is of convolution type. A convolution type sequence of polynomials has a unique associated operator called a delta operator. Such an operator is found for pn(0) (x), and its integral representation is developed. A convolution type sequence of polynomials may have associated Sheffer sequences of polynomials. The set of associated Sheffer sequences of the sequence pn(0)(x) is obtained, and is foundto be ℙ = {{pn(λ) (x)} =0 : λ ∈ R}. The major properties of these sequences of polynomials are studied.The polynomials {pn(λ) (x)}∞n=0, λ < 0, are not orthogonal polynomials on the real line with respect to any positive real measure for failing to satisfy Favard’s three term recurrence relation condition. For every λ ≤ 0, an associated nonstandard inner product is defined with respect to which pn(λ)(x) is orthogonal. Finally, the connection and linearization problems for the Symmetric Meixner-Pollaczek polynomials are solved. In solving the connection problem the convolution property of the polynomials is exploited, which in turn helps to solve the general linearization problem.
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| 4. |
- Hellström, Lars, 1974-
(author)
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The Diamond Lemma for Power Series Algebras
- 2002
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Doctoral thesis (other academic/artistic)abstract
- The main result in this thesis is the generalisation of Bergman's diamond lemma for ring theory to power series rings. This generalisation makes it possible to treat problems in which there arise infinite descending chains. Several results in the literature are shown to be special cases of this diamond lemma and examples are given of interesting problems which could not previously be treated. One of these examples provides a general construction of a normed skew field in which a custom commutation relation holds.There is also a general result on the structure of totally ordered semigroups, demonstrating that all semigroups with an archimedean element has a (up to a scaling factor) unique order-preserving homomorphism to the real numbers. This helps analyse the concept of filtered structure. It is shown that whereas filtered structures can be used to induce pretty much any zero-dimensional linear topology, a real-valued norm suffices for the definition of those topologies that have a reasonable relation to the multiplication operation.The thesis also contains elementary results on degree (as of polynomials) functions, norms on algebras (in particular ultranorms), (Birkhoff) orthogonality in modules, and construction of semigroup partial orders from ditto quasiorders.
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| 5. |
- Larsson, Leo, 1972-
(author)
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Carlson type inequalities and their applications
- 2003
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Doctoral thesis (other academic/artistic)abstract
- This thesis treats inequalities of Carlson type, i.e. inequalities of the form∥f∥x≤K∏i=1m∥f∥Aiθiwhere ∑i=1mθi =1 and K is some constant, independent of the function f. X and Ai are normed spaces, embedded in some Hausdorff topological vector space. In most cases, we have m=2, and the spaces involved are weighted Lebesgue spaces on some measure space. For example, the inequality∫0∞f(x)dx≤π∫0∞f2(x)dx1/4∫0∞x2 f2 (x)dx1/4first proved by F. Carlson, is the above inequality with m=2, θ1 =θ2 =1 2, X=L1(ℝ+, dx), A1 =L2 (ℝ+, dx) and A2 =L2 (ℝ+, x2 dx). In different situations, suffcient, and sometimes necessary, conditions are given on the weights in order for a Carlson type inequality to hold for some constant K. Carlson type inequalities have applications to e.g. moment problems, Fourier analysis, optimal sampling, and interpolation theory.
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| 6. |
- Strömberg, Fredrik, 1973-
(author)
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Computational Aspects of Maass Waveforms
- 2005
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Doctoral thesis (other academic/artistic)abstract
- The topic of this thesis is computation of Mass waveforms, and we consider a number of different cases: Congruence subgroups of the modular group and Dirichlet characters (chapter 1); congruence subgroups and general multiplier systems and real weight (chapter 2); and noncongruence subgroups (chapter 3). In each case we first discuss the necessary theoretical background. We then outline the algorithm and display some of the results obtained by it.
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| 7. |
- Carlsson, Linus, 1972-, et al.
(author)
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A note on B-envelope of holomorphy and B-extendable domains
- 2008
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In: Complex Variables and Elliptic Equations. - Abingdon, Oxon, UK : Taylor & Francis. - 1747-6933 .- 1747-6941. ; 53:4, s. 307-309
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Journal article (peer-reviewed)abstract
- Let B subset of H(infinity)(X) be a Banach Algebra on a Riemann domain X over C(n). We show that under certain conditions on B and X, all functions in B can be extended to functions in B(E(B, X)) where E(B, X) is the B-envelope of holomorphy.
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| 10. |
- Jain, P., et al.
(author)
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Inequalities and properties of some generalized Orlicz classes and spaces
- 2007
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In: Acta Mathematica Hungarica. - : Springer Science and Business Media LLC. - 0236-5294 .- 1588-2632. ; 117:1-2, s. 161-174
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Journal article (peer-reviewed)abstract
- We discuss and complement the knowledge about generalized Orlicz classes and Orlicz spaces X Φ obtained by replacing the space L 1 in the classical construction by an arbitrary Banach function space X. Our main aim is to focus on the task to study inequalities in such spaces. We prove a number of new inequalities and also natural generalizations of some classical ones (e.g., Minkowski’s, Hölder’s and Young’s inequalities). Moreover, a number of other basic facts for further study of inequalities and function spaces are included.
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