Tag: Factorization

Free Download Schur Parameters, Factorization and Dilation Problems By Tiberiu Constantinescu (auth.)
1995 | 254 Pages | ISBN: 3034899106 | PDF | 8 MB
This book is devoted to the ubiquity of the Schur parameters. A dilation theoretic view leads to a unified perspective on several topics where Schur parameters appear as basic cells. Together with the transmission line, their physical counter- part, they appear in scattering theory, in modeling, prediction and filtering of nonstationary processes, in signal processing, geophysics and system theory. Modeling problems are considered for certain classes of operators, interpolation problems, determinental formulae, as well as connections with certain classes of graphs where, again, the Schur parameters could play a role. Some general algorithms that explore the transmission line are also presented in this book. As a whole, the text is self-contained and it is addressed to people interested in the previously mentioned topics or connections between them.

Free Download Gilles Pisier, "Factorization of Linear Operators and Geometry of Banach Spaces "
English | ISBN: 0821807102 | | 154 pages | PDF | 5 MB
This book surveys the considerable progress made in Banach space theory as a result of Grothendieck’s fundamental paper Resumé de la théorie métrique des produits tensoriels topologiques. The author examines the central question of which Banach spaces $X$ and $Y$ have the property that every bounded operator from $X$ to $Y$ factors through a Hilbert space, in particular when the operators are defined on a Banach lattice, a $C^*$-algebra or the disc algebra and $H^\infty$. He reviews the six problems posed at the end of Grothendieck’s paper, which have now all been solved (except perhaps the exact value of Grothendieck’s constant), and includes the various results which led to their solution. The last chapter contains the author’s construction of several Banach spaces such that the injective and projective tensor products coincide; this gives a negative solution to Grothendieck’s sixth problem.

Free Download Primality Testing and Integer Factorization in Public-Key Cryptography by Song Y. Yan
English | PDF (True) | 2009 | 386 Pages | ISBN : 0387772677 | 5.3 MB
The Primality Testing Problem (PTP) has now proved to be solvable in deterministic polynomial-time (P) by the AKS (Agrawal-Kayal-Saxena) algorithm, whereas the Integer Factorization Problem (IFP) still remains unsolvable in (P). There is still no polynomial-time algorithm for IFP. Many practical public-key cryptosystems and protocols such as RSA (Rivest-Shamir-Adleman) rely their security on computational intractability of IFP.