Search results

In [[convex analysis]] and [[mathematical optimization]], the '''supporting functional''' is a generalization of the [[supporting hyperplane]] of a set. ...h>.<ref>{{cite book|title=Foundations of mathematical optimization: convex analysis without linearity|page=323|first1=Diethard|last1=Pallaschke|first2=Stefan|l ...

...book of [[Norbert Wiener]]. It is an orthogonal expansion for nonlinear [[functional (mathematics)|functionals]] closely related to the [[Volterra series]] and ...near system identification]]. In this context, the series approximates the functional relation of the output to the entire history of system input at any time. ...

In [[mathematics]] &ndash; specifically, in [[functional analysis]] &ndash; a '''Bochner-measurable function''' taking values in a [[Banach s | title = Monotone operators in Banach space and nonlinear partial differential equations ...

...ath>X^*</math> (see <ref name="ST">S. Solimini, C. Tintarev, Concentration analysis in Banach spaces, Comm. Contemp. Math. 2015, DOI 10.1142/S0219199715500388< ...S. Solimini, C. Tintarev, On weak convergence in metric spaces, Nonlinear Analysis and Optimization (B. S. Mordukhovich, S. Reich, A. J. Zaslavski, Editors), ...

...ers–Ulam–Rassias stability problem |journal=Banach Journal of Mathematical Analysis |date=January 2007 |volume=1 |issue=1 |pages=11–22 |doi=10.15352/bjma/12403 ..., [https://www.springer.com/mathematics/book/978-1-4614-3497-9 ''Nonlinear Analysis. Stability, Approximation, and Inequalities. In honor of Themistocles M. Ra ...

...23b2065-479d-4ee5-92de-85ddf4ce6ec2}}</ref> MSPC can be used to quantify [[nonlinear]] phase coupling between a set of base frequencies and their [[harmonic]]/[ [[Category:Nonlinear functional analysis]] ...

{{Short description|Theorem in convex analysis}} ...[mathematics]], the '''bipolar theorem''' is a [[theorem]] in [[functional analysis]] that characterizes the bipolar (that is, the [[Polar set|polar]] of the p ...

...=2205529|last=Du|first=Y.|title=Order structure and topological methods in nonlinear partial differential equations. Vol. 1. Maximum principles and applications {{Functional analysis}} ...

...e linearity assumption between the response (scalar or functional) and the functional linear predictor is replaced by an additivity assumption. ===Functional Additive Model=== ...

{{Short description|Type of regression analysis}} ...] and functional [[additive model]]s are three special cases of functional nonlinear models. ...

|title=Hyers–Ulam–Rassias Stability of Functional Equations in Nonlinear Analysis ...nctional Analysis]], [[Functional Equations]], [[Approximation Theory]], [[Analysis on Manifolds]], [[Calculus of Variations]], [[Inequality (mathematics)|Ineq ...

...g''.<ref name="Tao">Terence Tao, A pseudoconformal compactification of the nonlinear Schrödinger equation and applications, New York J. Math. '''15''' (2009), 2 ...in: Adimuri, K. Sandeep, I. Schindler, C. Tintarev, editors, Concentration Analysis and Applications to PDE ICTS Workshop, Bangalore, January 2012, {{ISBN|978- ...

...on''' or '''Lyapunov–Schmidt construction''' is used to study solutions to nonlinear equations in the case when the [[implicit function theorem]] does not work. be the given nonlinear equation, <math> X,\Lambda, </math> and <math> Y </math> are ...

...>{{cite book|last=Berberian|first=Sterling K.|title=Lectures in Functional Analysis and Operator Theory|series=Graduate Texts in Mathematics, No. 15|publisher= {{Functional analysis}} ...

...3=Maestre|first3=M.|author4=J. Schmets|title=Recent Progress in Functional Analysis|url=https://books.google.com/books?id=G4t3B7ZHtlgC&pg=PA4|accessdate=28 Jun ...-7515-7.pdf |title=Banach Space Theory: The Basis for Linear and Nonlinear Analysis |last2=Habala |first2=Petr |last3=Hájek |first3=Petr |last4=Montesinos&nbsp ...

{{Short description|Mathematical theorem in convex analysis}} ...me="Zalinescu">{{cite book |last=Zălinescu |first=Constantin |title=Convex analysis in general vector spaces |publisher=World Scientific Publishing&nbsp;Co.,&n ...

in the [[Spectrum (functional analysis)|spectrum]] <math>\sigma(A)</math> of a [[Unbounded_operator#Closed_linear_ |title=Methods of modern mathematical physics, vol. IV. Analysis of operators ...

...ps://core.ac.uk/download/pdf/82047336.pdf |journal=Journal of Mathematical Analysis and Applications |volume=50 |pages=66–73 |doi=10.1016/0022-247X(75)90038-4 ...edu/~burke/papers/reprints/22-diff-spec-abs-rad1994.pdf |journal=Nonlinear Analysis, Theory, Methods & Applications |volume=23 |issue=4 |pages=467–488 |doi=10. ...

==Functional components== ===Differential nonlinear responses to resources=== ...

...m theorem''' (or simply '''Lions's theorem''') is a result in [[functional analysis]] with applications in the study of [[partial differential equation]]s. It * (existence of a "weak inverse") for each [[continuous linear functional]] ''f''&nbsp;&isin;&nbsp;''V''^&lowast;, there is an element ''h' ...