In the early 1990s he sparked off a controversy with Paul A . Samuelson and Koiki Miyazaki in the " Oxford Economics Papers " on the validity of the Keynes-Kaldor-Pasinetti theorem of the Cambridge distribution theory.
22.
Although he published a series of interesting papers on distribution theory, density estimators etc . he was best known for his work on sequential analysis : International recognition found his monograph Sequential Tests of Statistical Hypotheses .
23.
Singular supports may also be used to understand phenomena special to distribution theory, such as attempts to'multiply'distributions ( squaring the Dirac delta function fails essentially because the singular supports of the distributions to be multiplied should be disjoint ).
24.
Literally any merely mediocre statistics doctoral program will require their students to do coursework in measure theory because it's required to fully understand the mechanics of tail events, distribution theory via Lebesgue integrals, and the like ( see measure-theoretic probability theory for more info ).
25.
Just as in the formulation of distribution theory, it is in practice regarded as a limit of a sequence of smooth functions; one may meaningfully take the Laplacian of a bump function, which is smooth by definition, and let the bump function approach the indicator in the limit.
26.
A later reformulation in a Bourbaki seminar by showed that parts of Tate's proof could be expressed by distribution theory : the space of distributions ( for Schwartz Bruhat test functions ) on the adele group of " K " transforming under the action of the ideles by a given ? has dimension 1.
27.
Pasinetti's purpose is therefore to offer an alternative paradigm and unify these theories in a new and solid set, which incorporates the contributions of models of Harrod and Domar and the distribution theory of the post-Keynesian economists in Cambridge : the whole lit and dotted with some of the theories, ideas and concerns of the classical economists.
28.
He extended the theory developed by Paul Vojta ( an analogy of the Nevanlinna theory, part of the value distribution theory of holomorphic functions, to diophantine geometry ) and applied the method of " dynamic diophantine approximation " which he developed in the process, to transcendental algebraic geometry ( and therefore for varieties over the complex numbers, where methods of complex analysis can be used ).
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