Bøker i Mathematics and Its Applicatio-serien

I. Measures and quasimeasures. Integration.- 1. Realvalued measures on algebras of sets.- 1.1. Premeasures.- 1.2. Same tests for ?-additivity of premeasures.- 1.3. Measurable and topological Radon spaces.- 1.4. Cylindrical measures.- 2. Cylinder sets and cylindrical functions.- 2.1. General definition of cylinder set.- 2.2. Cylinder sets in a linear space X.- 2.3. Measurable linear space.- 2.4. Cylindrical functions.- 3. Quasimeasures. Integration.- 3.1. Quasimeasures.- 3.2. Integral with respect to a quasimeasure.- 3.3. Quasimeasures in a measurable linear space.- 3.4. Positive quasimeasures.- 3.5. Integration of noncylindrical functions.- 4. Supplement: Some notions related to the topology of linear spaces.- 4.1. Prenorms.- 4.2. Locally convex spaces.- 4.3. Duality of linear spaces.- 4.4. Rigged Hilbert spaces.- 4.5. Polars.- 4.6. Nuclear topology.- 4.7. Compactness.- 5. Chapter I: Supplementary remarks and historical comments.- II. Gaussian measures in Hilbert space.- 1. Gaussian measures in finite-dimensional spaces.- 1.1. Characteristic functional and density.- 1.2. Computation of certain integrals.- 1.3. Integration by parts.- 1.4. Solution of the Cauchy problem.- 2. Gaussian measures in Hilbert space.- 2.1. ?-additivity for a Gaussian cylindrical measure.- 2.2. Some transformations of Gaussian measures in X.- 2.3. Computation of integrals.- 2.4. Gaussian cylindrical measures with arbitrary correlation operator.- 3. Measurable linear functionals and operators.- 3.1. Measurable linear functionals.- 3.2. Measurable linear operators.- 3.3. Integration by parts.- 3.4. Expansion into orthogonal polynomials.- 4. Absolute continuity of Gaussian measures.- 4.1. Equivalence of measures in a product space.- 4.2. Equivalence of Gaussian measures which differ by their means.- 4.3. Equivalence of Gaussian measures with distinct correlation operators.- 4.4. Absolute continuity of measures obtained from Gaussian measures by certain transformations of space.- 5. Fourier-Wiener transformation.- 5.1. Fourier transformation with respect to a Gaussian measure.- 5.2. Fourier-Wiener transformation of entire nmctions.- 5.3. Connection between the Fourier-Wiener transformation and orthogonal polynomials.- 6. Complexvalued Gaussian quasimeasures.- 6.1. Feynman integrals.- 6.2. Integration of analytic functionals.- 6.3. Computation of certain Feynman integrals.- 7. Chapter II: Supplementary re marks and historical comments.- III. Measures in linear topological spaces.- 1. ?-additivity conditions for nonnegative cylindrical measures in the space X' dual to a locally convex space X.- 1.1. Sufficient conditions for ?-additivity. Strong regularity.- 1.2. Necessary conditions for ?-additivityM.- 1.3. The Hilbert space case.- 1.4. Integral representations of the group of unitary operators.- 1.5. Continuous cylindrical measures.- 2. Sequences of Radon measures.- 2.1. Weak compaetness in a spaee of measures.- 2.2. Weak completeness of spaees of measures.- 2.3. Properties of R-spaces.- 2.4. Examples of R-spaces.- 2.5. Weak compaetness of a family of measures in a space X'.- 3. Chapter III: Supplementary remarks and historical comments.- IV. Differentiable measures and distributions.- 1. Differentiable functions, differentiable expressions.- 1.1. Derivatives of a vector function.- 1.2. Higher order derivatives.- 1.3. Linear differential expressions.- 1.4. Symmetrie and dissipative differential operators.- 2. Differentiable measures.- 2.1. Derivative of a measure.- 2.2. The logarithmie derivative.- 2.3. The derivative of a measure as an element of the dual space.- 2.4. Higher order derivatives.- 3. Distributions and generalized functions.- 3.1. Test functions and measures.- 3.2. Distributions. Operations on distributions.- 3.3. Generalized funetions and kernels.- 3.4. Fourier transformation of distributions.- 3.5. Differential expressions for distributions.- 4. Positive definiteness. Quasi-invariant distributions and bidistributions.- 4.1. Positive distri

1. Neuroanatomy of dopaminergic system in the human brain.- 2. Radioligands for PET studies of D2-receptors: butyrophenone and ergot derivatives.- 3. Radioligands for dopamine receptor PET studies: benzamides and ligands for dopamine D-1 receptors.- 4. Monoamine precursors in PET research - biochemical issues and functional significance.- 5. Quantitation problems in positron emission tomography (PET) as applied to the kinetic analysis of the striatum dopamine data.- 6. Investigation of the dopamine system with positron emission tomography: general issues in modeling.- 7. Modelisation: application to the D2 receptors.- 8. [18F] Fluorodopa uptake in brain.- 9. Dopamine reuptake sites: the issues.- 10. Movement disorders: the clinical issues.- 11. Non-human primate models of dopamine system disorders: understanding neurodegenerative diseases and testing new therapeutic strategies.- 12. The dopamine system and mental disorders: clinical and psychopharmacological overview.- 13. D2 dopamine receptors and schizophrenia.- 14. The assessment of central D2-dopanvne receptor occupancy with positron emission tomography in long-term medicated schizophrenic patients.- 15. Measurement of dopamine receptor occupancy: clinical issues.

1. Environmental policy making: an introduction.- A. Decision-Making.- 2. A spatial theoretic approach to environmental politics.- 3. Green legislative politics.- 4. Regulation or taxation.- 5. Decision making about the environment; the role of information.- B. Case-Studies.- 6. Transport policies and the environment: regulation and taxation.- 7. Road pricing: a logical failure.- 8. Dutch manure policy: the lack of economic instruments.- 9. Dutch manure policy: the role of information.- C. Institutions.- 10. The role of property rights in environmental protection.- 11. The ecological social contract.- 12. Mirror, mirror on the wall, who is the fairest of them all.- About the authors.- Author index.

In this book several connections between probability theory and wave propagation are explored. The connection comes via the probabilistic (or path integral) representation of both the (fixed frequency) Green functions and of the propagators -operators mapping initial into present time data. The formalism includes both waves in continuous space and in discrete structures. One of the main applications of the formalism developed is to inverse problems in wave propagation. Using the probabilistic formalism, the parameters of the medium and the surfaces determining the region of propagation appear explicitly in the path integral representation of the Green functions and propagators. This fact is what provides a useful starting point for inverse problem formulation.Audience: The book is suitable for advanced graduate students in the mathematical, physical or in the engineering sciences. The presentation is quite self-contained, and not extremely rigorous.