It isn't that they can't see Approach your problems from the solution. the right end and begin with It is that they can't see the the answers. Then one day, perhaps you will find the problem. final question. G. K. Chesterton. The Scandal 'The Hermit Clad in Crane of Father Brown 'The Point of a Pin'. Feathers' in R. van Gulik's The Chinese Maze l1urders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Inhaltsverzeichnis
1. Random Operators in Hilbert Space. - 1. Basic Definitions. - 2. Characteristic Functions of Random Operators. - 3. Convergence of Random Operators. - 2. Functions of Random Operators. - 4. Spectral Representation for Symmetric Random Operators. - 5. Equations with Symmetric Random Operators. - 6. Equations with Semi-Bounded Random Operators. - 3. Operator-Valued Martingales. - 7. Operator-Valued Martingale Sequences. - 8. Convergence of Infinite Products of Independent Random Operators. - 9. Continuous Operator-Valued Martingales. - 4. Stochastic Integrals and Equations. - 10. Stochastic Integrals with Respect to an X-Valued Martingale. - 11. Stochastic Integral with Respect to an Operator-Valued Martingale. - 12. Stochastic Operator Equations. - 5. Linear Stochastic Operator Equations. - 13. Generalization of the Stochastic Operator Integral. - 14. Linear Differential Operator Equations. - 15. Continuous Stochastic Semigroups.
