Примери за използване на Functionals на Английски и техните преводи на Български
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Theory of functionals.
More recently we have been studying the extremal metrics for these functionals.
His work is summarised in his book Theory of functionals and of Integral and Integro-Differential Equations(1930).
Riesz was to publish many papers in this journal,the first in 1922 being on Egorov's theorem on linear functionals.
He also gives the uniform boundedness principle for linear functionals, the Banach- Steinhaus theorem.
Mathematical manipulations of the wavefunction usually involve bra-ket notation which requires an understanding of complex numbers and linear functionals.
In 1907 he discovered an integral representation theorem for functionals on the space of quadratic Lebesgue integrable functions.
Mathematical manipulations of the wave function usually involve braÐket notation, which requires an understanding of complex numbers and linear functionals.
Levy processes, functionals based on Levy processes, spectral theory of non-selfadjoint Markov processes, Brownian motion in random environment.
In this work Caccioppoli began to investigate how to generalise Riesz 's theorem on the representation of linear functionals by extending the initial definition set.
He immediately started work developing his theory of functionals which led to his interest and later contributions in integral and integro-differential equations.
Provided that f is a linear function from a vector space to the underlying scalar field, the above linear maps are dual to each other, andin functional analysis both are called linear functionals.
In his dissertation of 1906, discussed above,he started a whole new area with his investigations of functionals on a metric space and formulated the abstract notion of compactness.
In 1993, together with V V Zhikov and S M Kozlov, Oleinik published a Russian work Averaging of differential operators andin the following year an English translation appeared with the title Homogenization of differential operators and integral functionals.
In the same year Caccioppoli considered the extension of the definition of linear functionals from the set of continuous functions to the set of Baire functions, anticipating a special case of the Hahn- Banach theorem.
He also worked on conformal mappings and potential theory, and he was led to study boundary value problems for partial differential equations andthe theory of various functionals connected with them.
There is the Hahn-Banach theorem on the extension of continuous linear functionals, the Banach-Steinhaus theorem on bounded families of mappings, the Banach-Alaoglu theorem, the Banach fixed point theorem and the Banach-Tarski paradoxical decomposition of a ball.
Schwartz's idea(in 1947) was to give a unified interpretation of all the generalized functions that had infiltrated analysis as(continuous)linear functionals on the space Cç of infinitely differentiable functions vanishing outside compact sets.
The authors of this paper are all students of De Giorgi and they describe his contributions to geometric measure theory, the solution of Hilbert 's XIXth problem in any dimension, the solution of the n-dimensional Plateau problem, the solution of the n-dimensional Bernstein problem, some results on partial differential equations in Gevrey spaces,convergence problems for functionals and operators, free boundary problems, semicontinuity and relaxation problems, minimum problems with free discontinuity set, and motion by mean curvature.
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