Patterns of Transcendence : Classical Myth in Marina Tsvetaeva's Poetry of the 1920s

This study examines the position and meaning of Classical mythological plots, themes and characters in the oeuvre of the Russian Modernist poet Marina Tsvetaeva (1892-1941). The material consists of lyric poems from the collection Posle Rossii (1928) and two longer lyrical tragedies, Ariadna (1924) and Fedra (1927). These works are examined in the context of Russian Modernism and Tsvetaeva s own poetic development, also taking into account the author s biography, namely, her correspondence with Boris Pasternak. Tsvetaeva s appropriations of the myths enter into a dialogue with the Classical tradition and with the earlier Russian and Western literary manifestations of the source material. Her Classical texts are inextricably linked with her own authorial myth, they are used to project both her ideas about poetry as well as the authored self of her poems. An important context for Tsvetaeva s application of the Classical myths is the concept of the Platonic ladder of Eros. This plot evokes the process of transcendence of the mortal subject into the immaterial realm and is applied by the author as an extended metaphor of the poet s birth. Emphasizing the dialectical movement between the earthly and the divine, Tsvetaeva s Classical personae foreground various positions of the individual between these two realms. By means of kaleidoscopic reformulations of similar metaphors and concepts, Tsvetaeva s mythological poems illustrate the poet s position between the material and the immaterial and the various consequences of this dichotomy on the creative mission. At the heart of Tsvetaeva s appropriation of the Sibyl, Phaedra, Eurydice and Ariadne is the tension between the body and disembodiment. The two lyrical tragedies develop the dichotomous worldview further, nevertheless emphasizing the dual perspective of the divine and the earthly realms: immaterial existence is often evaluated from a material perspective and vice versa. The Platonic subtext is central for Ariadna, focussing on Theseus development from an earthly hero to a spiritual one. Fedra concentrates on Phaedra s divinely induced physical passion, which is nevertheless evoked in a creative light.

Boundedness of weakly singular integral operators on domains

The monograph dissertation deals with kernel integral operators and their mapping properties on Euclidean domains. The associated kernels are weakly singular and examples of such are given by Green functions of certain elliptic partial differential equations. It is well known that mapping properties of the corresponding Green operators can be used to deduce a priori estimates for the solutions of these equations. In the dissertation, natural size- and cancellation conditions are quantified for kernels defined in domains. These kernels induce integral operators which are then composed with any partial differential operator of prescribed order, depending on the size of the kernel. The main object of study in this dissertation being the boundedness properties of such compositions, the main result is the characterization of their Lp-boundedness on suitably regular domains. In case the aforementioned kernels are defined in the whole Euclidean space, their partial derivatives of prescribed order turn out to be so called standard kernels that arise in connection with singular integral operators. The Lp-boundedness of singular integrals is characterized by the T1 theorem, which is originally due to David and Journé and was published in 1984 (Ann. of Math. 120). The main result in the dissertation can be interpreted as a T1 theorem for weakly singular integral operators. The dissertation deals also with special convolution type weakly singular integral operators that are defined on Euclidean spaces.

Integral Transformations of Volterra Gaussian Processes

We study integral representations of Gaussian processes with a pre-specified law in terms of other Gaussian processes. The dissertation consists of an introduction and of four research articles. In the introduction, we provide an overview about Volterra Gaussian processes in general, and fractional Brownian motion in particular. In the first article, we derive a finite interval integral transformation, which changes fractional Brownian motion with a given Hurst index into fractional Brownian motion with an other Hurst index. Based on this transformation, we construct a prelimit which formally converges to an analogous, infinite interval integral transformation. In the second article, we prove this convergence rigorously and show that the infinite interval transformation is a direct consequence of the finite interval transformation. In the third article, we consider general Volterra Gaussian processes. We derive measure-preserving transformations of these processes and their inherently related bridges. Also, as a related result, we obtain a Fourier-Laguerre series expansion for the first Wiener chaos of a Gaussian martingale. In the fourth article, we derive a class of ergodic transformations of self-similar Volterra Gaussian processes.