Functional analysis

Normed linear spaces. Contraction mapping theorem. Applications to differential and integral equations. Linear transformations. Product spaces and Fubini's theorem. Projection and self-adjoint operators. Gram-Schmidt orthonormalization. Fourier analysis.

Подобные документы

  • Finding common solutions of linear differential equations of the fourth order, the coefficients of which satisfy the system of three differential equations of the first order. The problem of conformal mapping of polygons, whose sides are arcs of circles.

    статья, добавлен 04.02.2017

  • Further, we found sufficient conditions on linear Volterra integro-differential equations of the third kind to be correct in analytical functions which generalize the well-known fact of correctness of a Volterra integral equation of the second kind.

    статья, добавлен 12.08.2020

  • A generalization of the classical theorem of T. Kato on similarity for sequences of projections in Hilbert spaces to the case of unconditional Schauder decompositions. Refinement of the theorem of V.N. Vizitei on the stability of Schauder decompositions.

    статья, добавлен 30.10.2016

  • The algorithm of the basic components of a linear analysis. Work on nonlinear PCA, or NLPCA, autoassociative's neural networks, principal curves and manifolds, kernel the combination's of these approaches. The problem areas that require research.

    статья, добавлен 08.02.2013

  • Characterization of symmetric linear functionals as the simplest polynomials. The proof of the theory that every symmetric continuous linear functional on the complex space L (0,1) can be represented as the Lebesgue integral, multiplied by a constant.

    статья, добавлен 25.03.2016

  • Approximations in Scientic Computation, сomputer Arithmetic, mathematical Software. Linear Systems, solving Linear Systems, Iterative Methods for Linear Systems. Linear Least Squares, eigenvalues and Singular Values, Nonlinear Equations, optimization.

    учебное пособие, добавлен 25.11.2013

  • Description of combinatorial DG-Hopf color cooperadic models for configuration spaces of points in the first quarter and in the N-gon. The proof version of the formality theorem of Kontsevich to the two subspaces in the vector space and for the morphism.

    курсовая работа, добавлен 27.08.2016

  • The study of optimal control problems for linear parabolic equations with unbounded coefficients in the main part of elliptic operator. The peculiarities of this type of equations. Setting of the optimal control problem and its preliminary analysis.

    статья, добавлен 23.06.2016

  • Tiling of the limit space under the action of a (self-similar) subgroup. Self-similar groups and their limit spaces. Subgroup tilings of limit spaces. Tilings of limit spaces of abelian and nilpotent groups. Functional analysis to nilpotent Lie groups.

    статья, добавлен 27.06.2016

  • Determining the extent of interpolated approximation spaces generated by regular elliptic operators on compact manifolds. Features and through the application of Jackson-Bernstein inequalities for spectral approximation regular elliptic operators.

    статья, добавлен 25.03.2016

  • The definition of real and complex vector spaces. The calculation of the reference type. Rules of addition and multiplication of scalars. The concept of subset. The direct sum of two subspaces. The calculation of the projection of the vector on the area.

    презентация, добавлен 13.04.2016

  • Basic formulas of combinatorial analysis. Theorem of addition of probabilities of incompatible events. Theorem of multiplication of probabilities. Bayes’s formulas. Mathematical operations over random variables. Properties of a distribution function.

    курс лекций, добавлен 27.10.2013

  • Thin and sparse metric spaces as asymptotic counterparts of discrete and very close to discrete metric spaces respectively. Classify thin metric spaces up to coarse equivalence. The types of sparse spaces and construct the spaces of distinct types.

    статья, добавлен 19.02.2016

  • The paper attempts to state and prove a completeness theorem for the system S5 of supplemented by first-order quantifiers and the sign of equality. The basic modal language. A general strategy for proving completeness theorems for quantified modal logics.

    статья, добавлен 10.09.2012

  • System of a quasidifferential equation with measures on the semiaxis. Linear differential operators generated by differential expressions. Asymptotics of a fundamental solution system for a quasidifferential equation with measures on the semiaxis.

    статья, добавлен 25.03.2016

  • Mathematics as a fundamental science. The place in its structure of differential equations is one of the most harmonious ways of knowing the universe. Study of the algorithm for constructing compartmental (SIR) models, based on differential equations.

    статья, добавлен 10.08.2022

  • The spectral properties of a fourth-order functional-differential operator with a summable potential are studied. The boundary conditions are separated. The solution of the functional-differential equation. The solution of the Volterra integral equation.

    статья, добавлен 14.08.2020

  • Proving of the theorem on a normal limit distribution of the normalized number of false solutions of a beforehand consistent system of nonlinear random equations over the field GF(2) with additional condition on the number of nonzero components.

    статья, добавлен 25.03.2016

  • Formulation of the lemma before solving the problem. The search for the principle of solving the paradox. Mathematical problem solving. Philosophical proof of the theorem. Justification of conclusions that can be applied in solving paradoxical problems.

    контрольная работа, добавлен 19.03.2024

  • Assessment of convergence result for the sequential procedure in the form of alternating maximization to the maximum likelihood estimation for a family of models - Generalized linear models. Variable Linear Regression procedure. Using techniques ALS.

    курсовая работа, добавлен 27.08.2016

  • Solving Linear Systems with the Inverse. Transposes and Symmetric Matrices. General Linear Systems. The Fundamental Matrix Subspaces. Minimization of Quadratic Functions. Computations in Orthogonal Bases. Orthogonal Polynomials and Least Squares.

    учебное пособие, добавлен 25.11.2013

  • Dynamic Modeling with Difference Equations. Linear Models of Structured Populations. Nonlinear Models of Interactions. Modeling Molecular Evolution. Constructing Phylogenetic Trees. Infectious Disease Modeling. Curve Fitting and Biological Modeling.

    учебное пособие, добавлен 25.11.2013

  • Examination of unlimited closed convex subsets of Banach space X, having the same recessive cone, and metric spaces, which they form with the Hausdorff metric. Receiving an analog of the theorem of approximation of convex compacts by normal polyhedrons.

    статья, добавлен 12.05.2018

  • Linear Principal Components. A linear model formulation. The Principal Curve and Surface models. Theory for principal curves and surfaces. Algorithmic details. Estimation of curves and surfaces. Gold assay pairs. Generalized linear principal components.

    дипломная работа, добавлен 08.02.2013

  • The theory of inverse problems for differential equations as fields of applied mathematics. In article attention that when training in the inverse problems for differential equations at students scientific and cognitive potential develops is paid.

    статья, добавлен 29.03.2021

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