Neural Foundations of Meaning and Threat Every action that we take is grounded in an elaborate web of beliefs and goals. Take the simple act of opening a door. Such an act depends on our beliefs about what lies beyond the door, as well as what is available to us in our current location. At an even more basic level, our attempt to open the door is rooted in a belief that we understand how a door...

The most general form of a linear continuous functional operation on a function f(x) continuous on (a, b) has been expressed by F. Rieszf as a Stieltjes integral of f(x) with respect to a function of bounded variation. By virtue of the extension theorem of Hahn,$ this result can be extended to the case where f(x) has discontinuities of the first kind on (a, b). In establishing this more general...

Consider a (nonnegative) measure dσ with support in the interval [a, b] such that the respective orthogonal polynomials, above a specific index `, satisfy a three-term recurrence relation with constant coefficients. We show that the corresponding Stieltjes polynomials, above the index 2` − 1, have a very simple and useful representation in terms of the orthogonal polynomials. As a result of thi...

The goal of the paper is to develop a Heine-Stieltjes theory for univariate linear differential operators of higher order. Namely, for a given linear ordinary differential operator d(z) = Pk i=1Qi(z) d dzi with polynomial coefficients set r = maxi=1,...,k(degQi(z)− i). If d(z) satisfies the conditions: i) r ≥ 0 and ii) degQk(z) = k + r we call it a non-degenerate higher Lamé operator. Following...

Let L (u, a), oo < u < + oo denote the Fourier-Stieltjes transform, 00 f eluoda(x), of a distribution function u(x), oo < x < + co . Thus if 00 /3(x) is the distribution function which is 0, J, 1 according as x -1 < x ,< 1, 1 < x, then L (u,,8) = cos u ; and so, if b is a positive constant, cos (u/b) is the transform of the distribution function /3(bx) . Hence, if a is a positive constant, the ...

We provide necessary and sufficient conditions for the existence of idempotents arbitrarily large norm in Fourier algebra $A(G)$ Fourier–Stieltjes $B(G)$ a locally compact group $G$. prove that

We announce the definition of the dual group, GB(^, of the Fourier-Stieltjes algebra, B(G), of a locally compact group G; and we state four main theorems culminating in the result that GB(G) is a locally compact topological group which is topological^ isomorphic to G. This result establishes an explicit dual relationship between a group and its Fourier-Stieltjes algebra. Moreover, this result e...

The Stieltjes constants γn are the coefficients appearing in the Laurent series of the Riemann zeta function at s = 1. We give a simple and efficient method to compute a p-bit approximation of γn with rigorous error bounds. Starting from an integral representation due to Blagouchine, we shift the contour to eliminate cancellation. The integral is then evaluated numerically in ball arithmetic us...

Abstract. The Stieltjes–Wigert polynomials, which correspond to an indeterminate moment problem on the positive half-line, are eigenfunctions of a second order q-difference operator. We consider the orthogonality measures for which the difference operator is symmetric in the corresponding weighted L-spaces. Under some additional assumptions these measures are exactly the solutions to the q-Pear...

We introduce the concept of Stieltjes integral of an operator-valued function with respect to the spectral measure associated with a normal operator. We give sufficient conditions for the existence of this integral and find bounds on its norm. The results obtained are applied to the Sylvester and Riccati operator equations. Assuming that the entry C is a normal operator, the spectrum of the ent...