Skip to content
Free planNo credit card requiredStart writing
AI for Research home
AI for Research home
Dashboard
Sign inGet started

Search 250 million research papers

Read the abstract, see who wrote it and who cites it, and get the citation in APA, MLA, Chicago or Harvard.

About 2,633 papers for “Vector-valued function”

vector-valued function pdf

jktikejr · Zenodo (CERN European Organization for Nuclear Research) · 2024

<pre><code>\n<p><strong>vector-valued function pdf</strong><br></p>\n<p>Rating: 4.8 / 5 (4377 votes)<br></p>\n<p>Downloads: 45782<br><br></p>\n <p>= = = = = \n<strong><a href="https://calendario2023.es/21Nr9y?keyword=vector-valued function pdf" target="_blank">CLICK HERE TO DOWNLOAD</a></strong>\n = = = = = <br><br></p>\n<p><br><br><br><br></p>\n<p><br><br><br><br></p>\n<p><br><br>Definition (Vector Function). The intersection of this line with the yz-plane occurs at x =This corresponds to t =, which yields this intersection point: (0, 1,) De nition. Let D be a set of real numbers. This observation leads to the concept of vector-valued functions of a real variable. r(t) = hf (t); g(t)i or r(t) = f (t)i + g(t)j: The domain of r is the set of all t for which both component functions are de Vector-valued bounded variation Vector-valued integration Vector-valued Holder condition Vector-valued regular functions Compactness and convergence in the space of vector-valued regular functionsBoundary properties of a class the vector-valued regular functions in S(O, 1) Vector-valued elliptic functions A general vector valued function r(t) has a number as an input and a vector of some xed dimension as its output. A vector function r(t) of a real variable t is a rule that assigns a unique vector to every value of t from D. The set D is ExampleFind where the tangent line to the curve:) intersects the yz-plane. We describe several ways of associating a geometric object, such as a curve A vector-valued function, also referred to as a vector function, is a mathematical function of one or more variables whose range is a set of multidimensional vectors or A vector function r(t) = hf(t),g(t),h(t)i is a function of one variable—that is, there is only one "input" value. If the outputs are two-dimensional, then there are component functions. x y z x y z x y z (I) (II) (III) x y z x y z x y z (IV) (V) (VI) Find the curve parameterized by each vector-valued function CALCULUS OF VECTOR-VALUED FUNCTIONS The concept of limits, continuity, differentiation, integration and their application in the context of vector-valued De nition. Vector-valued functions SamyTindel Purdue University Multivariatecalculus-MA MostlytakenfromCalculus, Early Transcendentals byBriggs-Cochran-Gillett-Schulz Samy In this chapter we provide an informal introduction to vector-valued functions of several variables. What makes vector functions more complicated than the functions Vector-Valued FunctionsHere are several curves. The point: (1, 1, 0) occurs at t =Here are the equations of the tangent line. A general vector valued function r(t) has a number as an input and a vector of some xed dimension as its output. (13) This is Jacobi's matrix of γ. f (t) and g(t) such that. If the outputs are two-dimensional, then there are At first sight one could think that a vector-valued function (instead of a scalar-valued one) would not bring so much new in the way of problems and theory. It has one column because m =Note that the velocity vector is just the We can extend to vector-valued functions the properties of the derivative that we presented in the Introduction to particular, the constant multiple rule, the Vector-valued functions SamyTindel Purdue University Multivariatecalculus-MA MostlytakenfromCalculus, Early Transcendentals byBriggs-Cochran-Gillett-Schulz Samy T. Vector-valued functions Multivariate calculus/ Using this de nition of a limit, we say that a vector-valued function is continuous at the point t= aif lim t!a r(t) = r(a): (15) A vector-valued function is continuous in an interval if it is continuous attqHtL FigureHeaviside step function all points in the interval. x y z x y z x y z (I) (II) (III) x y z x y z x y z (IV) (V) (VI) Find the curve parameterized by each vector-valued function A vector-valued function, also referred to as a vector function, is a mathematical function of one or more variables whose range is a set of multidimensional vectors or infinite-dimensional vectors. Just look at the vector of the parametric curve: dγ dt (a)˜ dγdt (a) dγ n dt (a). We can see what this means with an implicitly as the null set (or a level set) of a function g: D R3!R2, or parametrically as the range of a map: D R!RA surface in R3 can be de ned explicitly as the graph of a function f: R2!R, implicitly as the null set (or as a level set) of a function g: D R3!R, or parametrically as the range of a function ˙: D R2!R Vector-Valued FunctionsHere are several curves. The input of a vector-valued function could be a scalar or a vector Learning ObjectivesWrite an expression for the derivative of a vector-valued function.; Find the tangent vector at a point for a given position vector.; Find the unit tangent vector at a point for a given position vector and explain its significance can be described by an ordered triple of real-valued functions of time.</p></code></pre>

Cited by 0Open access

Bounds for Vector-Valued Function Estimation

Andreas Maurer, Massimiliano Pontil · arXiv (Cornell University) · 2016

We present a framework to derive risk bounds for vector-valued learning with a broad class of feature maps and loss functions. Multi-task learning and one-vs-all multi-category learning are treated as examples. We discuss in detail vector-valued functions with one hidden layer, and demonstrate that the conditions under which shared representations are beneficial for multi- task learning are equally applicable to multi-category learning.

Cited by 2Open access

Simpliciality of vector-valued function spaces

Ondřej F. K. Kalenda, Jiří Spurný · ArXiv.org · 2025

We investigate integral representation of vector-valued function spaces, i.e., of subspaces $H\subset C(K,E)$, where $K$ is a compact space and $E$ is a (real or complex) Banach space. We point out that there are two possible ways of generalizing representation theorems known from the scalar case -- either one may represent (all) functionals from $H^*$ using $E^*$-valued vector measures on $K$ (as it is done in the literature) or one may represent (some) operators from $L(H,E)$ by scalar measures on $K$ using the Bochner integral. These two ways lead to two different notions of simpliciality which we call `vector simpliciality' and `weak simpliciality'. It turns out that these two notions are in general incomparable. Moreover, the weak simpliciality is not affected by renorming the target space $E$, while vector simpliciality may be affected. Further, if $H$ contains constants, vector simpliciality is strictly stronger and admits several characterizations (partially analogous to the characterizations known in the scalar case). We also study orderings of measures inspired by C.J.K.~Batty which may be (in special cases) used to characterize $H$-boundary measures. Finally, we give a finer version of representation theorem using positive measures on $K\times B_{E^*}$ and characterize uniqueness in this case.

Cited by 0Open access

Frames and a vector-valued ambiguity function

John J. Benedetto, Jeffrey J. Donatelli · 2008

The setting is that of vector-valued codes of length N. The background for this setting is our construction of new complex valued constant amplitude zero autocorrelation codes (off dc) - CAZACs, which serve as coefficients for phase coded waveforms with prescribed ambiguity function behavior. Vector-valued CAZACs are relevant in light of vector sensor and MIMO technologies. The goal is to define the discrete vector-valued ambiguity function. Our notion of frame multiplication allows us to make this definition. The theory and relevance of such ambiguity functions is developed, including computation of code from received discrete vector-valued ambiguity function data.

Cited by 9

Regularity conditions for vector-valued function algebras

Barqi, Z., Abtahi, M. · arXiv (Cornell University) · 2023

We consider several notions of regularity, including strong regularity, bounded relative units, and Ditkin's condition, in the setting of vector-valued function algebras. Given a commutative Banach algebra $A$ and a compact space $X$, let $\mathcal{A}$ be a Banach $A$-valued function algebra on $X$ and let $\mathfrak{A}$ be the subalgebra of $\mathcal{A}$ consisting of scalar-valued functions. This paper is about the connection between regularity conditions of the algebra $\mathcal{A}$ and the associated algebras $\mathfrak{A}$ and $A$. That $\mathcal{A}$ inherits a certain regularity condition $P$ to $\mathfrak{A}$ and $A$ is the easy part of the problem. We investigate the converse and show that, under certain conditions, $\mathcal{A}$ receives $P$ form $\mathfrak{A}$ and $A$. The results apply to tensor products of commutative Banach algebras as they are included in the class of vector-valued function algebras.

Cited by 0Open access

Multipliers in continuous vector-valued function spaces

Juan Carlos Candeal Haro, H.C. Lai · Bulletin of the Australian Mathematical Society · 1992

We identify the multiplier space of continuous vector-valued function spaces as the bounded continuous multiplier-valued space in the strong topology.

Cited by 7Open access

A property in vector-valued function spaces

Kexin Zhao, Dongni Tan · arXiv (Cornell University) · 2020

This paper deals with a property which is equivalent to generalised-lushness for separable spaces. It thus may be seemed as a geometrical property of a Banach space which ensures the space to have the Mazur-Ulam property. We prove that if a Banach space $X$ enjoys this property if and only if $C(K,X)$ enjoys this property. We also show the same result holds for $L_\infty(μ,X)$ and $L_1(μ,X)$.

Cited by 0Open access

Multiplication operators on vector-valued function spaces

Hülya Duru, Arkady Kitover, Mehmet Orhon · Proceedings of the American Mathematical Society · 2013

Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E"> <mml:semantics> <mml:mi>E</mml:mi> <mml:annotation encoding="application/x-tex">E</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a Banach function space on a probability measure space <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis normal upper Omega comma normal upper Sigma comma mu right-parenthesis period"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi mathvariant="normal"> Ω </mml:mi> <mml:mo>,</mml:mo> <mml:mi mathvariant="normal"> Σ </mml:mi> <mml:mo>,</mml:mo> <mml:mi> μ </mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>.</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">(\Omega ,\Sigma ,\mu ).</mml:annotation> </mml:semantics> </mml:math> </inline-formula> Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding="application/x-tex">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a Banach space and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E left-parenthesis upper X right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">E(X)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be the associated Köthe-Bochner space. An operator on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E left-parenthesis upper X right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">E(X)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is called a multiplication operator if it is given by multiplication by a function in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L Superscript normal infinity Baseline left-parenthesis mu right-parenthesis period"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>L</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal"> ∞ </mml:mi> </mml:mrow> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:mi> μ </mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>.</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">L^{\infty }(\mu ).</mml:annotation> </mml:semantics> </mml:math> </inline-formula> In the main result of this paper, we show that an operator <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper T"> <mml:semantics> <mml:mi>T</mml:mi> <mml:annotation encoding="application/x-tex">T</mml:annotation> </mml:semantics> </mml:math> </inline-formula> on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E left-parenthesis upper X right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">E(X)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a multiplication operator if and only if <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper T"> <mml:semantics> <mml:mi>T</mml:mi> <mml:annotation encoding="application/x-tex">T</mml:annotation> </mml:semantics> </mml:math> </inline-formula> commutes with <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L Superscript normal infinity Baseline left-parenthesis mu right-parenthesis"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>L</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal"> ∞ </mml:mi> </mml:mrow> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:mi> μ </mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">L^{\infty }(\mu )</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and leaves invariant the cyclic subspaces generated by the constant vector-valued functions in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E left-parenthesis upper X right-parenthesis period"> <mml:semantics> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>.</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">E(X).</mml:annotation> </mml:semantics> </mml:math> </inline-formula> As a corollary we show that this is equivalent to <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper T"> <mml:semantics> <mml:mi>T</mml:mi> <mml:annotation encoding="application/x-tex">T</mml:annotation> </mml:semantics> </mml:math> </inline-formula> satisfying a functional equation considered by Calabuig, Rodríguez, and Sánchez-Pér

Cited by 3Open access