Motivated by a recent paper (Budd (2018)), where a new family of positive self-similar Markov processes associated to stable processes appears, we introduce a new family of Levy processes, called the double hypergeome...
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Motivated by a recent paper (Budd (2018)), where a new family of positive self-similar Markov processes associated to stable processes appears, we introduce a new family of Levy processes, called the double hypergeometric class, whose Wiener-Hopf factorisation is explicit, and as a result many functionals can be determined in closed form.
This paper concerns three classes of real-valued functions on intervals, operator monotone functions, operator convex functions, and strongly operator convex functions. Strongly operator convex functions were previous...
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This paper concerns three classes of real-valued functions on intervals, operator monotone functions, operator convex functions, and strongly operator convex functions. Strongly operator convex functions were previously treated in [3] and [4], where operator algebraic semicontinuity theory or operator theory were substantially used. In this paper we provide an alternate treatment that uses only operator inequalities (or even just matrix inequalities). We show also that if to is a point in the domain of a continuous function f, then f is operator monotone if and only if (f (t) - f (t(0)) / (t - t(0)) is strongly operator convex. Using this and previously known results, we provide some methods for constructing new functions in one of the three classes from old ones. We also include some discussion of completely monotone functions in this context and some results on the operator convexity or strong operator convexity of phi o f when f is operator convex or strongly operator convex. (C) 2018 Elsevier Inc. All rights reserved.
The purpose of the present paper is to investigate some structural and qualitative aspects of two different perturbations of the parameters of g-fractions. In this context, the concept of gap g-fractions is introduced...
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The purpose of the present paper is to investigate some structural and qualitative aspects of two different perturbations of the parameters of g-fractions. In this context, the concept of gap g-fractions is introduced. While tail sequences of a continued fraction play a significant role in the first perturbation, Schur fractions are used in the second perturbation of the g-parameters that is considered. Illustrations are provided using Gaussian hypergeometric functions. Using a particular gap g-fraction, some members of the class of pick functions are also identified.
We investigate the operator monotonicity of the following functions: f(t) = t(gamma) (t(alpha 1) - 1)(t(alpha 2) - 1) . . . (t(alpha n) - 1)/(t(beta 1) - 1)(t(beta 2) - 1) . . . (t(beta n) - 1) (t is an element of (0,...
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We investigate the operator monotonicity of the following functions: f(t) = t(gamma) (t(alpha 1) - 1)(t(alpha 2) - 1) . . . (t(alpha n) - 1)/(t(beta 1) - 1)(t(beta 2) - 1) . . . (t(beta n) - 1) (t is an element of (0, infinity)), where gamma is an element of R and alpha(i), beta(j) > 0 with alpha(i) not equal beta(j) (i, j = 1, 2, . . . , n). This property for these functions has been considered by V.E.S. Szabo [14]. (C) 2015 Published by Elsevier Inc.
A deep result of J. Lewis (1983) shows that the polylogarithms Li-alpha(z) := Sigma(infinity)(k = 1) z(k)/k(alpha) map the open unit disk D centered at the origin one-to-one onto convex domains for all alpha >= 0. ...
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A deep result of J. Lewis (1983) shows that the polylogarithms Li-alpha(z) := Sigma(infinity)(k = 1) z(k)/k(alpha) map the open unit disk D centered at the origin one-to-one onto convex domains for all alpha >= 0. In the present paper this result is generalized to the so-called universal convexity and universal starlikeness (with respect to the origin) in the slit-domain Lambda := C \ [1,infinity), introduced by S. Ruscheweyh, L. Salinas and T. Sugawa (2009). This settles a conjecture made in that work and proves, in particular, that Li-alpha(z) maps an arbitrary open disk or half-plane in. one-to-one onto a convex domain for every alpha >= 1.
For functions f whose Taylor coefficients at the origin form a Hausdorff moment sequence we study the behaviour of w(y) := vertical bar f(gamma + iy)vertical bar for y > 0 (gamma <= 1 fixed).
For functions f whose Taylor coefficients at the origin form a Hausdorff moment sequence we study the behaviour of w(y) := vertical bar f(gamma + iy)vertical bar for y > 0 (gamma <= 1 fixed).
In earlier works, authors such as Varga, Micchelli and Willoughby, Ando, and Fiedler and Schneider have studied and characterized functions which preserve the M-matrices or some subclasses of the M-matrices, such as t...
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In earlier works, authors such as Varga, Micchelli and Willoughby, Ando, and Fiedler and Schneider have studied and characterized functions which preserve the M-matrices or some subclasses of the M-matrices, such as the Stieltjes matrices. Here we characterize functions which either preserve the inverse M-matrices or map the inverse M-matrices to the M-matrices. In one of our results we employ the theory of pick functions to show that if A and B are inverse M-matrices such that B-1 <= A(-1), then (B + tI)(-1) <= (A + tI)(-1), for all t >= 0.
We solve the maximal value problem for the functional Re Sigma(j=1)(m)a(kj) in the class of functions f(z) = z + a(2)z(2) + ... that are holomorphic and univalent in the unit disk and satisfy the inequality \f(z)\ <...
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We solve the maximal value problem for the functional Re Sigma(j=1)(m)a(kj) in the class of functions f(z) = z + a(2)z(2) + ... that are holomorphic and univalent in the unit disk and satisfy the inequality \f(z)\ < M. We prove that the pick functions are extremal for this problem for sufficiently large M whenever the set of indices k(1),..., k(m) contains an even number.
Existence and uniqueness in law of reflecting Brownian motion in a wedge is proved. The direction of reflection along the sides of the wedge varies in a reasonable fashion, except perhaps at the corner.
Existence and uniqueness in law of reflecting Brownian motion in a wedge is proved. The direction of reflection along the sides of the wedge varies in a reasonable fashion, except perhaps at the corner.
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