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AN APPLICATION OF NONSTANDARD ANALYSIS TO CHARACTERS OF GROUPS OF CONTINUOUS FUNCTIONS
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An Introduction to Nonstandard Functional Analysis
1997In the following let V(X) be the full superstructure over an appropriate infinite set X containing ℂ and containing also the normed linear spaces we want to consider. Since sometimes we also have to look at Banach spaces which are not a priori in our superstructure we first of all prove the following helpful lemma. For an explicit application see 2.6.
M. Wolff
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Dirac Delta Functions Via Nonstandard Analysis
Canadian Mathematical Bulletin, 1975We recall that a Dirac delta function δ(x) in the real number system is the idealization of a function that vanishes outside a "short" interval and satisfies It is conceived as a function δ for which δ(0)=+ ∞, δ(t)=0 if t≠0, and This function should possess the "sifting property" for any continuous function f.
Lightstone, A. H., Wong, Kam
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A new class of Lyapunov functions for nonstandard switching systems: The stability analysis problem
IEEE Conference on Decision and Control and European Control Conference, 2011This paper presents a new class of Lur'e type Lyapunov functions for a discrete-time switched system interconnected with a switched nonlinearity satisfying a mode-dependent cone bounded condition. This function includes the mode-dependent nonlinearity, but not its integral.
Cavichioli Gonzaga, Carlos +3 more
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Nonstandard analysis applied to path integrals and generalized functions
Il Nuovo Cimento B Series 11, 1982A rigorous definition is given to the path integral over fields as a nonstandard object and by using stochastic fields. Nonstandard generalized functions are defined and these are identified with the moments of the field. The relation between generalized stochastic processes and nonstandard stochastic fields is also studied and a stochastic ...
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A Nonstandard Functional Programming Language
Asian Symposium on Programming Languages and Systems, 2017Hirofumi Nakamura +3 more
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Nonstandard Analysis and its Applications: INFINITESIMALS IN FUNCTIONAL ANALYSIS
, 1988C. Henson
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