Finite Rank Bargmann-Toeplitz Operators with Non-Compactly Supported Symbols

Theorems about characterization of finite rank Toeplitz operators in Fock-Segal-Bargmann spaces, known previously only for symbols with compact support, are carried over to symbols without that restriction, however with a rather rapid decay at infinity. The proof is based upon a new version of the Stone-Weierstrass approximation theorem

The 2-Hessian and sextactic points on plane algebraic curves

In an article from 1865, Arthur Cayley claims that given a plane algebraic curve there exists an associated 2-Hessian curve that intersects it in its sextactic points. In this paper we fix an error in Cayley's calculations and provide the correct defining polynomial for the 2-Hessian. In addition, we present a formula for the number of sextactic points on cuspidal curves and tie this formula to the 2-Hessian. Lastly, we consider the special case of rational curves, where the sextactic points appear as zeros of the Wronski determinant of the 2nd Veronese embedding of the curve.Comment: Updated version to be published in Mathematica Scandinavica. Substantially rewritten, but with essential results unchanged. Contains results from first author's master's thesis. 21 pages, 2 figure

Generalized Weierstrass representation for surfaces in multidimensional Riemann spaces

Generalizations of the Weierstrass formulae to generic surface immersed into $R^4$, $S^4$ and into multidimensional Riemann spaces are proposed. Integrable deformations of surfaces in these spaces via the modified Veselov-Novikov equation are discussed.Comment: LaTeX, 20 pages, minor misprints correcte