H.P. Lovecraft’s Philosophy of Science Fiction Horror

The paper is an examination and critique of the philosophy of science fiction horror of seminal American horror, science fiction and fantasy writer H.P. Lovecraft (1890-1937). Lovecraft never directly offers a philosophy of science fiction horror. However, at different points in his essays and letters, he addresses genres he labels “interplanetary fiction”, “horror”, “supernatural horror”, and “weird fiction”, the last being a broad heading covering both supernatural fiction and science fiction. Taken together, a philosophy of science fiction horror emerges. Central to this philosophy is the juxtaposition of the mysterious, unnatural and alien against a realistic background, in order to produce the emotion that Lovecraft calls “cosmic fear”. This background must not only be scientifically accurate, but must accurately portray human psychology, particularly when humans are faced with the weird and alien. It will be argued that Lovecraft’s prescriptions are overly restrictive and would rule out many legitimate works of science fiction horror art. However, he provides useful insights into the genre

Entire approximations for a class of truncated and odd functions

We solve the problem of finding optimal entire approximations of prescribed exponential type (unrestricted, majorant and minorant) for a class of truncated and odd functions with a shifted exponential subordination, minimizing the $L^1(\R)$-error. The class considered here includes new examples such as the truncated logarithm and truncated shifted power functions. This paper is the counterpart of the works of Carneiro and Vaaler (Some extremal functions in Fourier analysis, Part II in Trans. Amer. Math. Soc. 362 (2010), 5803-5843; Part III in Constr. Approx. 31, No. 2 (2010), 259--288), where the analogous problem for even functions was treated.Comment: 25 pages. To appear in J. Fourier Anal. App

Gaussian Subordination for the Beurling-Selberg Extremal Problem

We determine extremal entire functions for the problem of majorizing, minorizing, and approximating the Gaussian function $e^{-\pi\lambda x^2}$ by entire functions of exponential type. This leads to the solution of analogous extremal problems for a wide class of even functions that includes most of the previously known examples (for instance \cite{CV2}, \cite{CV3}, \cite{GV} and \cite{Lit}), plus a variety of new interesting functions such as $|x|^{\alpha}$ for $-1 < \alpha$; \,$\log \,\bigl((x^2 + \alpha^2)/(x^2 + \beta^2)\bigr)$, for $0 \leq \alpha < \beta$;\, $\log\bigl(x^2 + \alpha^2\bigr)$; and $x^{2n} \log x^2$\,, for $n \in \N$. Further applications to number theory include optimal approximations of theta functions by trigonometric polynomials and optimal bounds for certain Hilbert-type inequalities related to the discrete Hardy-Littlewood-Sobolev inequality in dimension one

Extremal functions in de Branges and Euclidean spaces

In this work we obtain optimal majorants and minorants of exponential type for a wide class of radial functions on $\mathbb{R}^N$. These extremal functions minimize the $L^1(\mathbb{R}^N, |x|^{2\nu + 2 - N}dx)$-distance to the original function, where $\nu >-1$ is a free parameter. To achieve this result we develop new interpolation tools to solve an associated extremal problem for the exponential function $\mathcal{F}_{\lambda}(x) = e^{-\lambda|x|}$, where $\lambda >0$, in the general framework of de Branges spaces of entire functions. We then specialize the construction to a particular family of homogeneous de Branges spaces to approach the multidimensional Euclidean case. Finally, we extend the result from the exponential function to a class of subordinated radial functions via integration on the parameter $\lambda >0$ against suitable measures. Applications of the results presented here include multidimensional versions of Hilbert-type inequalities, extremal one-sided approximations by trigonometric polynomials for a class of even periodic functions and extremal one-sided approximations by polynomials for a class of functions on the sphere $\mathbb{S}^{N-1}$ with an axis of symmetry

Be-Schichten. Fiktion und Realität in den Arbeiten von Heide Hatry.

In ihrer Performance Skin Room überführt die Konzeptkünstlerin Heide Hatry tierische Organe und andere Körperteile in neue Formen. In ihren folgenden Projekten – Heads and Tales und Not a Rose – transformiert sie diese zu ganz neuen Körpern. Ihre collagenhaft gefertigten Objekte werden von ihr arrangiert, inszeniert und fotografiert. Zusammen mit den Texten anderer Autoren, die sich auf Hatrys Arbeiten beziehen, werden die Collagen mit gleichsam immer neuen Schichten der Artifizialisierung bedeckt. Je mehr sich die Haut und das Fleisch von ihrem ursprünglichen Zustand entfernen, desto mehr wird der Betrachter dazu aufgefordert, sich mit seiner Aneignung von Bildern und seiner Teilhabe bei deren Beseelung auseinanderzusetzen

Hilbert spaces and the pair correlation of zeros of the Riemann zeta-function

Montgomery's pair correlation conjecture predicts the asymptotic behavior of the function $N(T,\beta)$ defined to be the number of pairs $\gamma$ and $\gamma'$ of ordinates of nontrivial zeros of the Riemann zeta-function satisfying $0<\gamma,\gamma'\leq T$ and $0 < \gamma'-\gamma \leq 2\pi \beta/\log T$ as $T\to \infty$. In this paper, assuming the Riemann hypothesis, we prove upper and lower bounds for $N(T,\beta)$, for all $\beta >0$, using Montgomery's formula and some extremal functions of exponential type. These functions are optimal in the sense that they majorize and minorize the characteristic function of the interval $[-\beta, \beta]$ in a way to minimize the $L^1\big(\mathbb{R}, \big\{1 - \big(\frac{\sin \pi x}{\pi x}\big)^2 \big\}\,dx\big)$-error. We give a complete solution for this extremal problem using the framework of reproducing kernel Hilbert spaces of entire functions. This extends previous work by P. X. Gallagher in 1985, where the case $\beta \in \frac12 \mathbb{N}$ was considered using non-extremal majorants and minorants.Comment: to appear in J. Reine Angew. Mat