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Summary

In Chapter 4, we take a limit where the coupling of the measurement apparatus to the quantum system is very small, and in this limit, discuss weak measurements and weak values. The later involved a sequence of a weak and a strong measurement. Generalizations of these effects are discussed using the concepts in Chapter 3, and we discuss generalized eigenvalues of quantum observables that can exceed the eigenvalue range and reincorporate the concept of observables in generalized measurement theory.

Summary

A spectral characterization of the Christoffel function is provided via its associated moment matrix, and that of Dirac measures. A first (Hahn-Banach) extension of the Christoffel function to Lp spaces is characterized. A second extension is also provided and analyzed where squares of polynomials (hence positive everywhere) are replaced by larger convex cones of polynomials positive on the support of the underlying measure, in particular polynomials in a certain associated quadratic module.

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4 - Weak Measurement

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10 - Spectral Characterization and Extensions of the Christoffel Function

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2 results

4 - Weak Measurement

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10 - Spectral Characterization and Extensions of the Christoffel Function

Summary