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- Ameur, Yacin, et al.
(författare)
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Interpolation classes and matrix monotone functions
- 2007
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Ingår i: Journal of operator theory. - 0379-4024 .- 1841-7744. ; 57:2, s. 409-427
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Tidskriftsartikel (refereegranskat)abstract
- An interpolation function of order n is a positive function -/+ on (0, infinity) such that vertical bar vertical bar -/+ (A)(1/2) T -/+ (A)-(1/2) vertical bar vertical bar <= max(vertical bar vertical bar T vertical bar vertical bar, vertical bar A(1/2)TA(-1/2) vertical bar vertical bar) for all n x ii matrices T and A such that A is positive definite. By a theorem of Donoghue, the class C-n of interpolation functions of order n coincides with the class of functions -/+ such that for each n-subset S = {lambda i}(n)(i=1)of (0,infinity) there exists a positive Pick function h on (0, co) interpolating -/+ at S. This note comprises a study of the classes C-n and their relations to matrix monotone functions of finite order. We also consider interpolation functions on general unital C*-algebras.
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| 2. |
- 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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| 3. |
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| 4. |
- Balkan, Andrew, et al.
(författare)
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Hardy spaces for the strip
- 2007
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Ingår i: Journal of Mathematical Analysis and Applications. - : Elsevier BV. - 0022-247X .- 1096-0813. ; 333:1, s. 347-364
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we shall study Hardy spaces of analytic functions in a strip S. Our main result is on one hand an intrinsic characterization of the spaces and on the second that polynomials are dense. We also present an orthogonal (in H-2(S)) basis of polynomials.
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| 5. |
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| 6. |
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| 7. |
- Ekstig, Kerstin, et al.
(författare)
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Sonja Lyttkens
- 2015
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Ingår i: Upsala Nya Tidning. - : Upsala nya tidning. - 1104-0173. ; 125:12, s. B13-B13
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Tidskriftsartikel (populärvet., debatt m.m.)abstract
- Sonja Lyttkens was born in 1919 and died in 2014. She was the second woman to get a PhD in mathematics in Sweden, and the first to become a university lecturer.
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| 8. |
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| 9. |
- Guo, Qi, 1957-
(författare)
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Minkowski Measure of Asymmetry and Minkowski Distance for Convex Bodies
- 2004
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis consists of four papers about the Minkowski measure of asymmetry and the Minkowski (or Banach-Mazur) distance for convex bodies.We relate these two quantities by giving estimates for the Minkowski distance in terms of the Minkowski measure. We also investigate some properties of the Minkowski measure, in particular a stability estimate is given. More specifically, let C and D be n-dimensional convex bodies. Denote by As(C) and As(D) the Minkowski measures of asymmetry of C and D resp. and by d(C,D) the Minkowski distance between C and D.In Paper I, by using a linearisation method for affine spaces and affine maps and using a generalisation of a lemma of D.R. Lewis, we proved that d(C,D) < n(As(C) + As(D))/2 for all convex bodies C,D.In Paper II, by first proving some general existence theorems for a class of volume-increasing affine maps, we obtain the estimate that under the same conditions as in paper I, d(C,D) < (n-1) min(As(C),As(D)) + n.In Paper III we consider the Minkowski measure itself. We determine the Minkowski measures for convex hulls of sets of the form conv(C,p) where C is a convex set with known measure of asymmetry and p is a point outside C.In Paper IV, we focus on estimating the deviation of a convex body C from the simplex S if the Minkowski measure of C is close to the maximum value n (known to be attained only for the simplex). We prove that if As(C) > n - ε for 0 < ε < 1/δ where δ = 8(n+1), then d(C,S) < 1 + 8(n+1) ε .
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| 10. |
- Janson, Svante, 1955-, et al.
(författare)
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Higher moments of Banach space valued random variables
- 2015
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Ingår i: Memoirs of the American Mathematical Society. - : American Mathematical Society (AMS). - 0065-9266 .- 1947-6221. ; 238:1127, s. 1-110
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Tidskriftsartikel (refereegranskat)abstract
- We define the k:th moment of a Banach space valued random variable as the expectation of its k: th tensor power; thus the moment (if it exists) is an element of a tensor power of the original Banach space. We study both the projective and injective tensor products, and their relation. Moreover, in order to be general and flexible, we study three different types of expectations: Bochner integrals, Pettis integrals and Dunford integrals. One of the problems studied is whether two random variables with the same injective moments (of a given order) necessarily have the same projective moments; this is of interest in applications. We show that this holds if the Banach space has the approximation property, but not in general. Several chapters are devoted to results in special Banach spaces, including Hilbert spaces, C(K) and D[0,1]. The latter space is non-separable, which complicates the arguments, and we prove various preliminary results on e.g. measurability in D[0,1] that we need. One of the main motivations of this paper is the application to Zolotarev metrics and their use in the contraction method. This is sketched in an appendix.
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