We invert the Fredholm equation representing the light scattered by a single spherical particle or a distribution of spherical particles to obtain the particle size distribution function and refractive index. We obtain the solution by expanding the distribution function as a linear combination of a set of orthonormal basis functions. The set of orthonormal basis functions is composed of Schmidt...

‎Given a frame of a separable Hilbert space $H$‎, ‎we present some‎ ‎iterative methods for solving an operator equation $Lu=f$‎, ‎where $L$ is a bounded‎, ‎invertible and symmetric‎ ‎operator on $H$‎. ‎We present some algorithms‎ ‎based on the knowledge of frame bounds‎, ‎Chebyshev method and conjugate gradient method‎, ‎in order to give some‎ ‎approximated solutions to the problem‎. ‎Then we i...

‎In this paper‎, ‎two iterative methods are constructed to solve the operator equation $ Lu=f $ where $L:Hrightarrow H $ is a bounded‎, ‎invertible and self-adjoint linear operator on a separable Hilbert space $ H $‎. ‎ By using the concept of frames of subspaces‎, ‎which is a generalization of frame theory‎, ‎we design some  algorithms based on Galerkin and Richardson methods‎, ‎and then we in...

<p style='text-indent:20px;'>The translation of an operator is defined by using conjugation with time-frequency shifts. Thus, one can define <inline-formula><tex-math id="M3">\begin{document}$ \Lambda $\end{document}</tex-math></inline-formula>-shift-invariant subspaces Hilbert-Schmidt operators, finitely generated, respect to a lattice id="M4">\begin{document}$...

Consider three normal operators A,B,C on a separable Hilbert space ? as well scalar-valued spectral measures ? A ?(A), B ?(B) and C ?(C). For any ??L ? (? ×? ) X,Y?S 2 (?), the of Hilbert–Schmidt ?, we provide general definition triple operator integral ? (?)(X,Y) belonging to S (?) in such way that (?) belongs (S (?)×S (?),S (?)) bounded bilinear resulting mapping :L )?B is w * -continuous iso...

The inequality in (a) is naturally the best possible. Theorem l(a) is connected with questions such as the Beck-Fiala theorem or the Koml6s conjecture (see [2J, [3J and [7]). Combinatorial motivations are presented exhaustively in [8J (see also [6]). In a slightly different form, Theorem l(a) was used in [IJ in the proof that nuclear Frechet spaces satisfy the Levy-Steinitz theorem on rearrange...

This paper deals with the problem of nonparametric independence testing, a fundamental decisiontheoretic problem that asks if two arbitrary (possibly multivariate) random variables X,Y are independent or not, a question that comes up in many fields like causality and neuroscience. While quantities like correlation of X,Y only test for (univariate) linear independence, natural alternatives like ...

We consider a conformal field theory for bosons on the Riemann sphere. Correlation functions are defined as singular limits of functional integrals. The main result is that these amplitudes define transition amplitudes, that is multilinear Hilbert-Schmidt functionals on a fixed Hilbert space.

This paper deals with bracket flows of Hilbert-Schmidt operators. We establish elementary convergence results for such flows and discuss some of their consequences.