| 1. |
- Araaya, Tsehaye, 1962-
(författare)
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The Symmetric Meixner-Pollaczek polynomials
- 2003
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)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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| 2. |
- Larsson, Leo, 1972-
(författare)
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Carlson type inequalities and their applications
- 2003
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)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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| 3. |
- Strömberg, Fredrik, 1973-
(författare)
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Computational Aspects of Maass Waveforms
- 2005
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)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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| 4. |
- Jain, P., et al.
(författare)
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Inequalities and properties of some generalized Orlicz classes and spaces
- 2007
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Ingår i: Acta Mathematica Hungarica. - : Springer Science and Business Media LLC. - 0236-5294 .- 1588-2632. ; 117:1-2, s. 161-174
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Tidskriftsartikel (refereegranskat)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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| 5. |
- Johansson, Anders, et al.
(författare)
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Square Summability of Variations and Convergence of the Transfer Operator
- 2008
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Ingår i: Ergodic Theory and Dynamical Systems. - 0143-3857 .- 1469-4417. ; 28:4, s. 1145-1151
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we study the one-sided shift operator on a state space defined by a finite alphabet. Using a scheme developed by Walters [P. Walters. Trans. Amer Math. Soc. 353(l) (2001), 327-347], we prove that the sequence of iterates of the transfer operator converges under square summability of variations of the g-function, a condition which gave uniqueness of a g-measure in our earlier work [A. Johansson and A. Oberg. Math. Res. Lett. 10(5-6) (2003), 587-601]. We also prove uniqueness of the so-called G-measures, introduced by Brown and Dooley [G. Brown and A. H. Dooley. Ergod. Th. & Dynam. Sys. 11 (1991), 279-307], under square summability of variations.
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| 6. |
- Kuliev, K., et al.
(författare)
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An extension of Rothe´s method to noncylindrical domains
- 2007
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Ingår i: Applications of Mathematics. - : Institute of Mathematics, Czech Academy of Sciences. - 0862-7940 .- 1572-9109. ; 52:5, s. 365-389
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Tidskriftsartikel (refereegranskat)abstract
- In this paper Rothe's classical method is extended so that it can be used to solve some linear parabolic boundary value problems in non-cylindrical domains. The corresponding existence and uniqueness theorems are proved and some further results and generalizations are discussed and applied.
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| 7. |
- Nyström, Kaj, 1969-, et al.
(författare)
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On Monte Carlo algorithms applied to Dirichlet problems for parabolic operators in the setting of time-dependent domains
- 2009
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Ingår i: Monte Carlo Methods and Applications. - Berlin New York : de Gruyter. - 1569-3961. ; 15, s. 11-47
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Tidskriftsartikel (refereegranskat)abstract
- Dirichlet problems for second order parabolic operators in space-time domains Ω⊂ Rn+1 are of paramount importance in analysis, partial differential equations and applied mathematics. These problems can be approached in many different ways using techniques from partial differential equations, potential theory, stochastic differential equations, stopped diffusions and Monte Carlo methods. The performance of any technique depends on the structural assumptions on the operator, the geometry and smoothness properties of the space-time domain Ω, the smoothness of the Dirichlet data and the smoothness of the coefficients of the operator under consideration. In this paper, which mainly is of numerical nature, we attempt to further understand how Monte Carlo methods based on the numerical integration of stochastic differential equations perform when applied to Dirichlet problems for uniformly elliptic second order parabolic operators and how their performance vary as the smoothness of the boundary, Dirichlet data and coefficients change from smooth to non-smooth. Our analysis is set in the genuinely parabolic setting of time-dependent domains, which in itself adds interesting features previously only modestly discussed in the literature. The methods evaluated and discussed include elaborations on the non-adaptive method proposed by Gobet [4] based on approximation by half spaces and exit probabilities and the adaptive method proposed in [3] for weak approximation of stochastic differential equations.
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| 8. |
- Okpoti, Christopher, et al.
(författare)
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An equivalence theorem for some integral conditions with general measures related to Hardy´s inequality
- 2007
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Ingår i: Journal of Mathematical Analysis and Applications. - : Elsevier BV. - 0022-247X .- 1096-0813. ; 326:1, s. 398-413
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Tidskriftsartikel (refereegranskat)abstract
- It is proved that, besides the usual Muckenhoupt condition, there exist four different scales of conditions for characterizing the Hardy type inequality with general measures for the case 1<pq<∞. In fact, an even more general equivalence theorem of independent interest is proved and discussed.
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| 9. |
- Persson, Lars-Erik, et al.
(författare)
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Some scales of equivalent weight characterizations of Hardy´s inequality: the case q < p
- 2007
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Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 10:2, s. 267-279
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Tidskriftsartikel (refereegranskat)abstract
- We consider the weighted Hardy inequality 1/q 1/p q ∞ ∞ x f p (x)v(x)dx f (t)dt u(x)dx C 0 0 0for the case 0 < q < p < ∞, p > 1 . The weights u(x) and v(x) for which this inequalityholds for all f (x) 0 may be characterized by the Mazya-Rosin or by the Persson-Stepanovconditions. In this paper, we show that these conditions are not unique and can be supplementedby some continuous scales of conditions and we prove their equivalence. The results for the dualoperator which do not follow by duality when 0 < q < 1 are also given.
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| 10. |
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