# Introduction to Function Space

Sentence Examples

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### Keywords frequently search together with Function Space

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## Function Space sentence examples within continuous time problem

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The proposed continuous-time problem is solved in a finite-dimensional function space spanned by Bernstein polynomials, which converts the problem into a solvable mixed-integer linear programming problem.

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A function space-based method is developed to solve the proposed model, which converts the continuous-time problem into a mixed-integer linear programming problem with finite dimensional decision space.

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## Function Space sentence examples within measurable set valued

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The first aim of this work is to introduce a new function space called the measurable set-valued Borel functions space and new topological space called the confine measurable set-valued Borel function topology on the set of the measurable set-valued Borel functions.

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## Function Space sentence examples within Banach Function Space

## Function Space sentence examples within Appropriate Function Space

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These spaces are the appropriate function spaces for the study of estimates on Besov type spaces and the end-point maximal regularity estimates for the fractional power H α in the sense that similar estimates might fail with the classical Besov spaces.

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## Function Space sentence examples within Modular Function Space

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In this paper, we introduce the notion of ρ-attractive elements in modular function spaces.

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In this paper, the explicit multistep, explicit multistep-SP and implicit multistep iterative sequences are introduced in the context of modular function spaces and proven to converge to the fixed point of a multivalued map T such that PρT, an associate multivalued map, is a ρ-contractive-like mapping.

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## Function Space sentence examples within Weighted Function Space

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In these operators, σ not only features the sequences of operators but also features the Korovkin function set { 1 , σ , σ 2 } $\lbrace 1,\sigma ,\sigma ^{2} \rbrace $ in a weighted function space such that the operators fix exactly two functions from the set.

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Motivated by earlier work of Korobov from 1963 and 1982, we present two variants of search algorithms for good lattice rules and show that the resulting rules exhibit a convergence rate in weighted function spaces that can be arbitrarily close to the optimal rate.

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## Function Space sentence examples within Valued Function Space

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As applications, we obtain that the above operators are bounded on the mixed radial-angular spaces, on the vector-valued mixed radial-angular spaces and on the vector-valued function spaces.

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The main result of this paper is an intersection representation for a class of anisotropic vector-valued function spaces in an axiomatic setting \`a la Hedberg$\&$Netrusov, which includes weighted anisotropic mixed-norm Besov and Triebel-Lizorkin spaces.

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## Function Space sentence examples within Holomorphic Function Space

## Function Space sentence examples within Dimensional Function Space

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The proposed continuous-time problem is solved in a finite-dimensional function space spanned by Bernstein polynomials, which converts the problem into a solvable mixed-integer linear programming problem.

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A recently proposed method by Mauroy and Goncalves is based on lifting the data snapshots into a suitable finite dimensional function space and identification of the infinitesimal generator of the Koopman semigroup.

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## Function Space sentence examples within Objective Function Space

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One of the main advantages of our proposal are both its simplicity and its ability to scale up (in objective function space).

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In addition, this approach identifies a diverse set of solutions in the multi-objective function space which can be challenging to estimate with single-objective formulations.

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## Function Space sentence examples within Variou Function Space

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As an application of this result, we obtain Korovkin-type approximation for Toeplitz operators acting on various function spaces including Bergman space $$A^{2}({\mathbb {D}})$$
, Fock space $$F^{2}({\mathbb {C}})$$
etc.

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The topological structure of the set of (weighted) composition operators has been studied on various function spaces on the unit disc such as Hardy spaces, the space of bounded holomorphic functions, weighted Banach spaces of holomorphic functions with sup-norm, Hilbert Bergman spaces.

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## Function Space sentence examples within General Function Space

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As an application, we give a characterization for the boundedness of the Volterra integral operator $$J_{g}$$ from $$\mathcal{L}_{p,\lambda}$$ to general function spaces $$F(p,p-1-\lambda,s)$$.

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Meanwhile, the boundedness, compactness, and essential norm of Volterra integral operators from Dirichlet type spaces D p p−� to general function spaces are also investigated.

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## Function Space sentence examples within Suitable Function Space

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The results rely on quantitative unique continuation estimates in suitable function spaces with explicit frequency dependence.

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It is shown that the marginal function of the considered control system is lower semi-continuous and the optimal states operator generates a continuous branch in a suitable function space.

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## Function Space sentence examples within Different Function Space

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Nonlinear fractional differential equations have been intensely studied using fixed point theorems on various different function spaces.

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In this paper, we obtain some inequalities about commutators of a rough p -adic fractional Hardy-type operator on Herz-type spaces when the symbol functions belong to two different function spaces.

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## Function Space sentence examples within Hilbert Function Space

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Here, we present a bio-inspired global stochastic optimisation method applicable in Hilbert function spaces.

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The properties of Hilbert function space of integrable functions and pointwise sections of measurable sets are considered through the application of integral representation of product vector measures, inner product functions and products of measurable sets.

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## Function Space sentence examples within Continuou Function Space

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Using operator-valued Ċα -Fourier multiplier results on vector-valued Hölder continuous function spaces and the Carleman transform, we characterize the Cα -well-posedness of second order degenerate differential equations with infinite delay: (Mu)′′(t) = Au(t)+ ∫ t −∞ a(t− s)Au(s)ds+ f (t) and (Mu′)′(t) = Au(t)+ ∫ t −∞ a(t−s)Au(s)ds+ f (t) on R, where A : D(A)→ X and M : D(M)→ X are closed linear operators in a complex Banach space X , and a ∈ L(R+)∩L(R+; tα dt).

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In this paper, by using operator-valued ${\dot{C}}^{\unicode[STIX]{x1D6FC}}$
-Fourier multiplier results on vector-valued Holder continuous function spaces, we give a characterization of the $C^{\unicode[STIX]{x1D6FC}}$
-well-posedness for the third order differential equations $au^{\prime \prime \prime }(t)+u^{\prime \prime }(t)=Au(t)+Bu^{\prime }(t)+f(t)$
, ( $t\in \mathbb{R}$
), where $A,B$
are closed linear operators on a Banach space $X$
such that $D(A)\subset D(B)$
, $a\in \mathbb{C}$
and $0<\unicode[STIX]{x1D6FC}<1$.

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## Function Space sentence examples within Test Function Space

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In the variational forms we introduce, the solution space is defined as a subspace V of the graph space associated with the differential operator in question, whereas the test function space L is a tuple of L 2 spaces that separately enforce the equation, boundary conditions of characteristic type, and initial conditions.

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Scalar and vector basis functions for the phase space \(\Omega \) (realizations of a turbulent flow) and the test function space \(\mathcal{N}_p\) (argument functions of the characteristic functional) plus analytic functions, for the purpose of testing numerically the convergence properties of the bases, are constructed using cylindrical coordinates suitable for the periodic flow through straight pipes with circular cross section.

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## Function Space sentence examples within Gevrey Function Space

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We establish the well-posedness of the MHD boundary layer system in Gevrey function space without any structural assumption.

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We first establish the existence and uniqueness of solution in Gevrey function spaces $$G_{\sigma ,s}^{r}({\mathbb {R}}^{N})$$
, then with the definition modulus of continuity, we show that the solution of Euler system is continuously dependent of the initial data $$v_{0}$$
in $$G_{\sigma ,s}^{r}({\mathbb {R}}^{N})$$.

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## Function Space sentence examples within Relevant Function Space

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We construct the relevant function space, which is significantly constrained due to the extended Steinmann relations, up to weight 13 in coproduct form, and up to weight 12 as an explicit polylogarithmic representation.

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Under an additional sub-exponential growth condition on the graph, we prove analyticity, ultracontractivity, and pointwise kernel estimates for these semigroups; we also show that their generators' spectra coincide on all relevant function spaces and present a Kreĭn-type dimension reduction, showing that their spectral values are determined by the spectra of generalized discrete Laplacians acting on various spaces of functions supported on combinatorial graphs.

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## Function Space sentence examples within Proper Function Space

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The proper function spaces and assumptions are proposed to discuss the existence of mild solutions.

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A proper function space setting is provided by a new weighted version of the Pohozaev–Trudinger inequality which enables us to prove the existence of variational, in particular finite energy solutions to (<jats:italic>C</jats:italic>).

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## Function Space sentence examples within Certain Function Space

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Recently, the authors developed a mathematical framework for the computation of optimal reaction coordinates of such systems that is based on learning a parametrization of a low-dimensional transition manifold in a certain function space.

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To unveil the inverse and composition properties of the IF operators, certain function spaces with their characterizations are presented and analyzed.

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## Function Space sentence examples within Analytic Function Space

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In this current manuscript, some general classes of weighted analytic function spaces in a unit disc are defined and studied.

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In this paper we are concerned with the global well-posedness of solutions to magnetohydrodynamics (MHD) boundary layer equations in analytic function spaces.

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## Function Space sentence examples within Normed Function Space

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The Volterra operator is defined on an arbitrary normed function space F d that is continuously embedded in the space of square integrable functions defined on the unit d -cube.

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This paper will introduce you to some properties of normed function spaces with many groups variables field of Analysis and it helps me appreciate how normed Lebesgue–Morrey space with many groups of variables that build and studied new normed spaces nowadays.

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## Function Space sentence examples within Classical Function Space

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This includes the basic definitions and properties of classical function spaces and distributions, the Fourier transform and the definition of Hadamard's finite part integrals which, in fact, represent the natural regularization of homogeneous distributions and of the hypersingular boundary integral operators.

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We characterize the reducing subspaces of S 2 ⁎ S 1 or S 1 S 2 ⁎ as wandering subspaces with additional structures, and give a unified way to describe the reducing subspaces of Toeplitz operators induced by non-analytic monomial on weighted Hardy spaces of several variables, which including many classical function spaces, such as weighted Bergman space and Dirichlet space over the polydisk.

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## Function Space sentence examples within Type Function Space

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In this paper, based on generalized Herz-type function spaces K̇ q (θ) were introduced by Y.

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It not only develops a theory of Sobolev type function spaces on metric measure spaces but also develops applications to Carnot-Carathéodory spaces, subelliptic equations, analysis on topological manifolds, potential theory on infinite graphs, and analysis on fractals.

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## Function Space sentence examples within Corresponding Function Space

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We develop a mathematical analysis of Navier–Stokes-like problems with a dynamic slip boundary condition, which requires a proper generalization of the Gelfand triplet and the corresponding function space setting.

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The classes of acceptable variations are described by convex cones in corresponding function spaces.

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## Function Space sentence examples within Scoring Function Space

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These results find theoretical support in the application of the concept of scoring function space.

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OBJECTIVE
Our purpose here is to review some the of methods used to calculate the electrostatic energy of protein-drug complexes and explore the capacity of these approaches for the generation of new computational tools for drug discovery using the abstraction of scoring function space.

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## Function Space sentence examples within Harmonic Function Space

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On harmonic function spaces, we define shift operators using zonal harmonics and partial derivatives, and develop their basic properties.

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We define the Kelvin-Mobius transform of a function harmonic on the unit ball of R n and determine harmonic function spaces that are invariant under this transform.

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## Function Space sentence examples within function space integral

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We investigate the behavior of the partial derivative approach to the change of scale formula and prove relationships among the analytic Wiener integral and the analytic Feynman integral of the partial derivative for the function space integral.

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In this paper we investigated a relationship between the analytic generalized Fourier–Feynman transform associated with Gaussian process and the function space integral for exponential type functionals on the function space $$C_{a,b}[0,T]$$ C a , b [ 0 , T ].

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## Function Space sentence examples within function space setting

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For the model, the history function space setting is a main difficulty because the usual space setting will lead the shift semigroup to be a unbounded semigroup.

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We develop a mathematical analysis of Navier–Stokes-like problems with a dynamic slip boundary condition, which requires a proper generalization of the Gelfand triplet and the corresponding function space setting.

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## Function Space sentence examples within function space solution

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A function space solution method is proposed to reduce the dimensionality of the continuous-time problem by modeling the parameter and decision trajectories in a function space formed by Bernstein polynomials, which converts the continuous-time problem into a linear programming problem.

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