**Author**: Alexander Constantine Bacopoulos

**Publisher:**

**ISBN:** WISC:89010832236

**Category:** Approximation

**Page:** 122

**View:** 212

*This work deals with the many variations of the Stoneileierstrass Theorem for vector-valued functions and some of its applications. The book is largely self-contained.*

**Author**:

**Publisher:** Elsevier

**ISBN:** 0080871364

**Category:** Mathematics

**Page:** 218

**View:** 534

*Bacopoulos, A., Godini, G., Singer, I., “On best approximation in vector-valued *

norms”, Colloq. ... I., “On infima of sets in the plane and best approximation,

simultaneous and vectorial, in a linear space with two norms”, in: Frehse, J.,

Pallaschke, ...

**Author**: Johannes Jahn

**Publisher:** Springer Science & Business Media

**ISBN:** 9783540248286

**Category:** Business & Economics

**Page:** 465

**View:** 543

*There is a difference, however, since in (3.4) the Hilbert space norm || || is used
since we are dealing with a vector valued kernel. In order to apply transference
methods to this more general situation we can use the following result: (3.6) The
...*

**Author**: Butzer

**Publisher:** Birkhäuser

**ISBN:** 9783034871808

**Category:** Science

**Page:** 685

**View:** 525

**Vector**-**valued** Functions. ... Let B be a compact set and let C,(B) be the **linear**

**space** of all m-dimensional vectors f=(f1, f2, ..., f,) whose components are ... (3.19)

The following theorems hold for **approximation** in the sense of the **norm** (3.19).

**Author**: Günter Meinardus

**Publisher:** Springer Science & Business Media

**ISBN:** 9783642856433

**Category:** Juvenile Nonfiction

**Page:** 202

**View:** 390

*9 Vector Approximation Vector approximation problems are abstract
approximation problems where a vectorial norm is used instead of a usual ( real -
valued ) norm . Many important results known from approximation theory can be
extended ...*

**Author**: Johannes Jahn

**Publisher:** Peter Lang Gmbh, Internationaler Verlag Der Wissenschaften

**ISBN:** UOM:39015017194500

**Category:** Linear topological spaces

**Page:** 310

**View:** 934

*the " distance of a point to a subset of a linear space endowed with a ( vector - *

valued ) norm with values in RP . ... normed linear space , G a non - void subset

of E and se € E . An element go e G is called an element of best approximation of

x ...

**Author**:

**Publisher:**

**ISBN:** STANFORD:36105001370878

**Category:** Mathematics

**Page:**

**View:** 204

*A normed vector space is an ordinary vector space equipped with a norm, a well-*

behaved function that assigns a nonnegative "length" to each vector. Basic

topological concepts ... The chapter highlights the idea of approximation through

mean value theorems, which allow us to estimate the increments of a function in

terms of increments of the approximating linear transformation. In Chapter 6 we

prove ...

**Author**: Mustafa A. Akcoglu

**Publisher:** John Wiley & Sons

**ISBN:** 9780470148242

**Category:** Mathematics

**Page:** 465

**View:** 766

*... Singer , I . : On best approximation in vector valued norms . Collog . Math . Soc *

. Ianos Bolyai 19 . Fourier Analysis and Approx . Theory , ( 1976 ) . 89 - 100 .

Bacopoulos , A . and Singer , I . : On convex vectorial optimization in linear

spaces .

**Author**: George Isac

**Publisher:** Peter Lang Pub Incorporated

**ISBN:** UOM:39015032533740

**Category:** Mathematics

**Page:** 136

**View:** 962

*Namely , following [ 1 ] , one can consider on E the " norm ” with values in the
plane R2 ( with its natural partial ordering ) , defined ... with values in partially
ordered linear spaces see e.g. [ 7 ] ) and to call an element 80 € G an element of
best vectorial approximation of x ... that VG ( x ) = g ( x ) may also happen for the
vector - valued norm ( 5 ) , namely , in the particular case when llolly = 11 • 112 =
|| • 1 ) .*

**Author**: György Alexits

**Publisher:**

**ISBN:** UCSC:32106008634146

**Category:** Approximation theory

**Page:** 926

**View:** 227

*4 ) the Hilbert space norm | | | | is used since we are dealing with a vector valued *

kernel . In order to apply transference methods to this more general situation we

can use the following result : LP ( R ) having ( 3 . 6 ) The Hilbert space valued ...

**Author**: Paul Leo Butzer

**Publisher:**

**ISBN:** UCAL:B4407422

**Category:** Approximation theory

**Page:** 685

**View:** 367

*A continuation of the authors' previous book, Isometries on Banach Spaces: Vector-valued Function Spaces and Operator Spaces, Volume Two covers much of the work that has been done on characterizing isometries on various Banach spaces.*

**Author**: Richard J. Fleming

**Publisher:** CRC Press

**ISBN:** 1420010204

**Category:** Mathematics

**Page:** 248

**View:** 484

*Let E be a lienar space over the ( real or complex ) field K endomed with a (
vector - valued ) norm 1 : 1 with values in the plane R ? ( with ... ( the distance of a
point to a subset of a normed linear space ) for the subsets of the plane R ?, DIST
( .*

**Author**:

**Publisher:**

**ISBN:** CORNELL:31924000749857

**Category:** Approximation theory

**Page:**

**View:** 444

*... ( 2006d : 41041 ) 41465 46E15 Stepanets , A . I . ( UKR - AOS ; Kiev ) Extremal
problems of approximation theory in linear spaces . ... It is shown that a simple
modification of the qd - algorithm makes it possible to construct the
homogeneous multivariate Padé ... ( 3 ) Co ( T , X ) , for a locally compact
Hausdorff space T , equipped with the strict topology defined by all weighted
seminorms of the form Pw : C ...*

**Author**:

**Publisher:**

**ISBN:** UOM:39015065183553

**Category:** Mathematics

**Page:**

**View:** 534

**approximation**. A variety of problems involving **vector spaces** and **linear**

operators can only be addressed if we can measure the ... A **norm** is a real-

**valued** function defined on a **vector space** that defines the size of the **vectors** in

the **space**.

**Author**: Mark S. Gockenbach

**Publisher:** CRC Press

**ISBN:** 9781439882870

**Category:** Mathematics

**Page:** 672

**View:** 866

*As before , lfl stands for the norm of f when f e B. In case B is an inner product
space , this norm can be taken to be the one induced by the inner product . Also ,
in case B is only a normed linear space , in the proof of Theorem 4.4 the
assertion ...*

**Author**: Avram Sidi

**Publisher:**

**ISBN:** NASA:31769000601453

**Category:**

**Page:** 25

**View:** 728

*... Volterra series, such as its convergence, approximation of a digital nonlinear
system by the discrete Volterra series, and so on. All the ... Here, for the first time
in this book, the first notion of the functional analysis is introduced, that is, of the
norm of a vector, and of a vector-valued sequence. ... linear space of which
elements are vectors, or scalar- or vectorvalued sequences, normed space,
metric space, ...*

**Author**: Andrzej Borys

**Publisher:** CRC Press

**ISBN:** 1420038443

**Category:** Technology & Engineering

**Page:** 312

**View:** 730

*Typical examples are scalar or vector valued functions defined on complex 2 or 3
dimensional meshes. Grosso et al. presented a method for mesh optimization
based on finite elements approximations with the L? norm and adaptive local
mesh refinement. ... In this paper we present a technique based on linear
approximations in Hilbert spaces and the finite element method to generate
sequences of ...*

**Author**: H.-C. Hege

**Publisher:** Springer Science & Business Media

**ISBN:** 3540639918

**Category:** Mathematics

**Page:** 393

**View:** 769

*JUST NON - METABELIAN GROUPS are shown to have close relations to
simultaneous approximations . ... Harry W . McLaughlin The problem we consider
is the approximation of m elements ( x1 , . . . , xm ) in a normed linear space by
one element in a subset of that normed linear space . ... It has been shown that
more flexibility is achieved by using generalized spaces where the norm is vector
valued .*

**Author**:

**Publisher:**

**ISBN:** STANFORD:36105119277668

**Category:** Dissertations, Academic

**Page:**

**View:** 688