126 research outputs found
Witten Index and spectral shift function
Let be a selfadjoint unbounded operator on a Hilbert space and let be a one parameter norm continuous family of self-adjoint bounded operators that converges in norm to asymptotes . Then setting one can consider the operator on the Hilbert space . We present a connection between the theory of spectral shift function for the pair of the asymptotes and index theory for the operator . Under the condition that the operator is a -relative trace-class perturbation of and some additional smoothness assumption we prove a heat kernel formula for all , where is a straight path joining and . Using this heat kernel formula we obtain the description of the Witten index of the operator in terms of the spectral shift function for the pair . {\bf Theorem.} \textit{If\, is a right and a left Lebesgue point of the spectral shift function for the pair (denoted by and , respectively), then the Witten index of the operator exists and equals } We note that our assumptions include the cases studied earlier. In particular, we impose no assumption on the spectra of and we can treat differential operators in any dimension. As a corollary of this theorem we have the following result. {\bf Corollary.} \textit{Assume that the asymptotes are boundedly invertible. Then the operator is Fredholm and for the Fredholm index of the operator we have where denotes the spectral flow along the path
Eisenstein and Tarkovsky
EISENSTEIN AND TARKOVSKY: AN UNEXPECTED CONNECTION For the majority of film scholars, the names of Tarkovsky and Eisenstein represent an opposition between two radically different approaches to the art of cinema. This opposition has been established by Tarkovsky himself, when he wrote: I am radically opposed to the way Eisenstein used the frame to codify intellectual formulae. My own method of conveying experience to the audience is quite different. Of course it has to be said that Eisenstein wasn't trying to convey his own experience to anyone, he wanted to put across ideas, purely and simply; but for me that sort of cinema is utterly inimical. Moreover, Eisenstein's montage dictum, as I see it, contradicts the very basis of the unique process whereby a film affects the audience.(1) Here, Tarkovsky was referring to Eisenstein's earlier films such as Strike, Battleship Potemkin, and October, all made in..
On the Number of Degrees of Freedom of Band-Limited Functions
Publication in the conference proceedings of SampTA, Bremen, Germany, 201
Models of New Femininity and Masculinity in Soviet Russia in the 1920s
STARS OF EARLY AMERICAN CINEMA AS MODELS OF NEW FEMININITY AND MASCULINITY IN SOVIET RUSSIA IN THE 1920S This paper explores some of the cinematic links that existed in the 1920s between Soviet Russia and its great "Other", America. It argues that in that decade, stars of silent American cinema, in particular Douglas Fairbanks Sr., Pearl White, and Mary Pickford offered the Soviet viewers, as well as critics and filmmakers, alternative models of new masculinity and femininity. For Soviet Russia in the 1920s, America became a kind of measuring stick of success(1) on the road toward the new, technologically advanced and efficient Soviet society. While the communist future was not yet attained, and the country was undergoing a process of massive transformation, the adjective "American" acquired a new meaning: it became a metaphor for excellence(2) and led to the appearance and wide use of the discursive practice..
On a conjectured property of the Witten index and an application to Levinson's theorem
A few years ago Fritz Gesztesy raised the issue of whether there was a
composition rule for the Witten index analogous to that satisfied by Fredholm
operators. In this note we prove a result in this direction and provide an
application to Levinson's theorem
Derivations on symmetric quasi-Banach ideals of compact operators
Let be symmetric quasi-Banach ideals of compact operators on
an infinite-dimensional complex Hilbert space , let be a
space of multipliers from to . Obviously, ideals
and are quasi-Banach algebras and it is clear that
ideal is a bimodule for . We study the set of all
derivations from into . We show that any such
derivation is automatically continuous and there exists an operator
such that , moreover
, where is the modulus of concavity of the quasi-norm
. In the special case, when is a
symmetric Banach ideal of compact operators on our result yields the
classical fact that any derivation on may be written
as , where is some bounded operator on and
.Comment: 21 page
- β¦