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Journal articles on the topic 'Vector valued functions'

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Published: 4 June 2021
Last updated: 25 July 2024

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1

Matkowski, Janusz. "Mean-value theorem for vector-valued functions." Mathematica Bohemica 137, no. 4 (2012): 415–23. http://dx.doi.org/10.21136/mb.2012.142997.

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2

Carmichael, Richard D. "Vector-Valued Analytic Functions Having Vector-Valued Tempered Distributions as Boundary Values." Axioms 12, no. 11 (November 6, 2023): 1036. http://dx.doi.org/10.3390/axioms12111036.

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Vector-valued analytic functions in Cn, which are known to have vector-valued tempered distributional boundary values, are shown to be in the Hardy space Hp,1≤p<2, if the boundary value is in the vector-valued Lp,1≤p<2, functions. The analysis of this paper extends the analysis of a previous paper that considered the cases for 2≤p≤∞. Thus, with the addition of the results of this paper, the considered problems are proved for all p,1≤p≤∞.
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3

Bonet, J., E. Jordá, and M. Maestre. "Vector-valued meromorphic functions." Archiv der Mathematik 79, no. 5 (November 2002): 353–59. http://dx.doi.org/10.1007/pl00012457.

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4

Bagheri-Bardi, G. A. "Vector-valued measurable functions." Topology and its Applications 252 (February 2019): 1–8. http://dx.doi.org/10.1016/j.topol.2018.11.002.

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5

He, Jianxun, and Shouyou Huang. "Constructions of Vector-Valued Filters and Vector-Valued Wavelets." Journal of Applied Mathematics 2012 (2012): 1–18. http://dx.doi.org/10.1155/2012/130939.

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Leta =(a1,a2,…,am)∈ℂmbe anm-dimensional vector. Then, it can be identified with anm×mcirculant matrix. By using the theory of matrix-valued wavelet analysis (Walden and Serroukh, 2002), we discuss the vector-valued multiresolution analysis. Also, we derive several different designs of finite length of vector-valued filters. The corresponding scaling functions and wavelet functions are given. Specially, we deal with the construction of filters on symmetric matrix-valued functions space.
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6

Domański, Paweł, and Michael Langenbruch. "Vector Valued Hyperfunctions and Boundary Values of Vector Valued Harmonic and Holomorphic Functions." Publications of the Research Institute for Mathematical Sciences 44, no. 4 (2008): 1097–142. http://dx.doi.org/10.2977/prims/1231263781.

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7

Roy, S. K., and N. D. Chakraborty. "Integration of vector-valued functions with respect to an operator-valued measure." Czechoslovak Mathematical Journal 36, no. 2 (1986): 198–209. http://dx.doi.org/10.21136/cmj.1986.102084.

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8

Cichoń, Dariusz, and Harold S. Shapiro. "Toeplitz operators in Segal-Bargmann spaces of vector-valued functions vector-valued functions." MATHEMATICA SCANDINAVICA 93, no. 2 (December 1, 2003): 275. http://dx.doi.org/10.7146/math.scand.a-14424.

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We discuss new results concerning unbounded Toeplitz operators defined in Segal-Bargmann spaces of (vector-valued) functions, i.e. the space of all entire functions which are square summable with respect to the Gaussian measure in $\mathrm{C}^n$. The problem of finding adjoints of analytic Toeplitz operators is solved in some cases. Closedness of the range of analytic Toeplitz operators is studied. We indicate an example of an entire function inducing a Toeplitz operator, for which the space of polynomials is not a core though it is contained in its domain.
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9

Carmichael, Richard D. "Cauchy Integral and Boundary Value for Vector-Valued Tempered Distributions." Axioms 11, no. 8 (August 10, 2022): 392. http://dx.doi.org/10.3390/axioms11080392.

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Using the historically general growth condition on scalar-valued analytic functions, which have tempered distributions as boundary values, we show that vector-valued analytic functions in tubes TC=Rn+iC obtain vector-valued tempered distributions as boundary values. In a certain vector-valued case, we study the structure of this boundary value, which is shown to be the Fourier transform of the distributional derivative of a vector-valued continuous function of polynomial growth. A set of vector-valued functions used to show the structure of the boundary value is shown to have a one–one and onto relationship with a set of vector-valued distributions, which generalize the Schwartz space DL2′(Rn); the tempered distribution Fourier transform defines the relationship between these two sets. By combining the previously stated results, we obtain a Cauchy integral representation of the vector-valued analytic functions in terms of the boundary value.
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10

Banakh, Iryna, Taras Banakh, and Kaori Yamazaki. "Extenders for vector-valued functions." Studia Mathematica 191, no. 2 (2009): 123–50. http://dx.doi.org/10.4064/sm191-2-2.

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11

Frerick, Leonhard, and Enrique Jordá. "Extension of vector-valued functions." Bulletin of the Belgian Mathematical Society - Simon Stevin 14, no. 3 (September 2007): 499–507. http://dx.doi.org/10.36045/bbms/1190994211.

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12

Carmichael, Richard D. "Generalized Vector-Valued Hardy Functions." Axioms 11, no. 2 (January 20, 2022): 39. http://dx.doi.org/10.3390/axioms11020039.

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We consider analytic functions in tubes Rn+iB⊂Cn with values in Banach space or Hilbert space. The base of the tube B will be a proper open connected subset of Rn, an open connected cone in Rn, an open convex cone in Rn, and a regular cone in Rn, with this latter cone being an open convex cone which does not contain any entire straight lines. The analytic functions satisfy several different growth conditions in Lp norm, and all of the resulting spaces of analytic functions generalize the vector valued Hardy space Hp in Cn. The analytic functions are represented as the Fourier–Laplace transform of certain vector valued Lp functions which are characterized in the analysis. We give a characterization of the spaces of analytic functions in which the spaces are in fact subsets of the Hardy functions Hp. We obtain boundary value results on the distinguished boundary Rn+i{0¯} and on the topological boundary Rn+i∂B of the tube for the analytic functions in the Lp and vector valued tempered distribution topologies. Suggestions for associated future research are given.
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13

Bector, C. R., and Riccardo Cambini. "Generalizedb-invex vector valued functions." Journal of Statistics and Management Systems 5, no. 1-3 (January 2002): 141–73. http://dx.doi.org/10.1080/09720510.2002.10701055.

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14

Micchelli, Charles A., and Massimiliano Pontil. "On Learning Vector-Valued Functions." Neural Computation 17, no. 1 (January 1, 2005): 177–204. http://dx.doi.org/10.1162/0899766052530802.

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In this letter, we provide a study of learning in a Hilbert space of vector-valued functions. We motivate the need for extending learning theory of scalar-valued functions by practical considerations and establish some basic results for learning vector-valued functions that should prove useful in applications. Specifically, we allow an output space Y to be a Hilbert space, and we consider a reproducing kernel Hilbert space of functions whose values lie in Y. In this setting, we derive the form of the minimal norm interpolant to a finite set of data and apply it to study some regularization functionals that are important in learning theory. We consider specific examples of such functionals corresponding to multiple-output regularization networks and support vector machines, for both regression and classification. Finally, we provide classes of operator-valued kernels of the dot product and translation-invariant type.
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15

Arendt, Wolfgang, and Nicolai Nikolski. "Vector-valued holomorphic functions revisited." Mathematische Zeitschrift 252, no. 3 (November 24, 2005): 687–89. http://dx.doi.org/10.1007/s00209-005-0858-x.

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16

Arendt, W., and N. Nikolski. "Vector-valued holomorphic functions revisited." Mathematische Zeitschrift 234, no. 4 (August 1, 2000): 777–805. http://dx.doi.org/10.1007/s002090050008.

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17

Bhatnagar, Savita. "Vector Valued Multipliers of McShane Integrable Functions." Journal of the Indian Mathematical Society 89, no. 1-2 (January 27, 2022): 08. http://dx.doi.org/10.18311/jims/2022/29294.

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We study the algebra of vector valued multipliers of Banach algebra valued McShane integrable functions. We prove that if <em>X</em> is a commutative Banach algebra, with identity <em>e</em> of norm one, then functions associated with measures of strong bounded variation and the set {L<sup>?</sup>([a, b],?) e} are vector valued multipliers of McShane integrable functions. We find some necessary and another set of sufficient conditions for a functiong to define a multiplier. In case X satisfies Radon Nikodym property (weak Radon Nikodym property), we study multiplier operators.
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18

NIKOU, AZADEH, and ANTHONY G. O'FARRELL. "BANACH ALGEBRAS OF VECTOR-VALUED FUNCTIONS." Glasgow Mathematical Journal 56, no. 2 (August 13, 2013): 419–26. http://dx.doi.org/10.1017/s0017089513000359.

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AbstractWe introduce the concept of an E-valued function algebra, a type of Banach algebra that consists of continuous E-valued functions on some compact Hausdorff space, where E is a Banach algebra. We present some basic results about such algebras, having to do with the Shilov boundary and the set of peak points of some commutative E-valued function algebras. We give some specific examples.
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19

Amenta, Alex, Emiel Lorist, and Mark Veraar. "Rescaled extrapolation for vector-valued functions." Publicacions Matemàtiques 63 (January 1, 2019): 155–82. http://dx.doi.org/10.5565/publmat6311905.

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20

Oppezzi, P., and A. Maria Rossi. "A convergence for vector valued functions." Optimization 57, no. 3 (June 2008): 435–48. http://dx.doi.org/10.1080/02331930601129624.

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21

Arendt, Wolfgang. "Vector-valued holomorphic and harmonic functions." Concrete Operators 3, no. 1 (April 28, 2016): 68–76. http://dx.doi.org/10.1515/conop-2016-0007.

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AbstractHolomorphic and harmonic functions with values in a Banach space are investigated. Following an approach given in a joint article with Nikolski [4] it is shown that for bounded functions with values in a Banach space it suffices that the composition with functionals in a separating subspace of the dual space be holomorphic to deduce holomorphy. Another result is Vitali’s convergence theorem for holomorphic functions. The main novelty in the article is to prove analogous results for harmonic functions with values in a Banach space.
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22

Ames, W. F., and C. Brezinski. "Vector-valued functions and their applications." Mathematics and Computers in Simulation 35, no. 2 (April 1993): 188. http://dx.doi.org/10.1016/0378-4754(93)90020-u.

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23

Sudakov, V. N. "Decomposition of vector-valued additive functions." Journal of Soviet Mathematics 61, no. 1 (August 1992): 1926–30. http://dx.doi.org/10.1007/bf01362807.

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24

Bukhvalov, A. V. "Sobolev spaces of vector-valued functions." Journal of Mathematical Sciences 71, no. 1 (August 1994): 2173–79. http://dx.doi.org/10.1007/bf02111291.

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25

Zhang, Chuanyi. "Vector-valued pseudo almost periodic functions." Czechoslovak Mathematical Journal 47, no. 3 (September 1997): 385–94. http://dx.doi.org/10.1023/a:1022492014464.

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26

Khurana, Surjit Singh. "Uniform measures on vector-valued functions." Publicationes Mathematicae Debrecen 55, no. 1-2 (July 1, 1999): 73–82. http://dx.doi.org/10.5486/pmd.1999.1932.

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27

RAJA, MATÍAS, and JOSÉ RODRÍGUEZ. "SCALAR BOUNDEDNESS OF VECTOR-VALUED FUNCTIONS." Glasgow Mathematical Journal 54, no. 2 (December 12, 2011): 325–33. http://dx.doi.org/10.1017/s0017089511000620.

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AbstractWe provide sufficient conditions for a Banach space-valued function to be scalarly bounded, which do not require to test on the whole dual space. Some applications in vector integration are also given.
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28

NIKOU, AZADEH, and ANTHONY G. O’FARRELL. "BANACH ALGEBRAS OF VECTOR-VALUED FUNCTIONS." Glasgow Mathematical Journal 62, no. 3 (September 6, 2019): 746. http://dx.doi.org/10.1017/s0017089519000351.

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29

Shigekawa, Ichiro. "LpContraction Semigroups for Vector Valued Functions." Journal of Functional Analysis 147, no. 1 (June 1997): 69–108. http://dx.doi.org/10.1006/jfan.1996.3056.

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30

Farkas, Eva C. "Approximation of vector valued smooth functions." Mathematische Nachrichten 271, no. 1 (July 2004): 15–21. http://dx.doi.org/10.1002/mana.200310179.

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31

Frerick, Leonhard, Enrique Jordá, and Jochen Wengenroth. "Extension of bounded vector-valued functions." Mathematische Nachrichten 282, no. 5 (April 16, 2009): 690–96. http://dx.doi.org/10.1002/mana.200610764.

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32

Qu, Feifei, Xin Wei, and Juan Chen. "Uncertainty principle for vector-valued functions." AIMS Mathematics 9, no. 5 (2024): 12494–510. http://dx.doi.org/10.3934/math.2024611.

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<abstract><p>The uncertainty principle for vector-valued functions of $ L^2({\mathbb{R}}^n, {\mathbb{R}}^m) $ with $ n\ge 2 $ are studied. We provide a stronger uncertainty principle than the existing one in literature when $ m\ge 2 $. The phase and the amplitude derivatives in the sense of the Fourier transform are considered when $ m = 1 $. Based on these definitions, a generalized uncertainty principle is given.</p></abstract>
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33

Wang, Chao, Ravi P. Agarwal, and Donal O'Regan. "Calculus of fuzzy vector-valued functions and almost periodic fuzzy vector-valued functions on time scales." Fuzzy Sets and Systems 375 (November 2019): 1–52. http://dx.doi.org/10.1016/j.fss.2018.12.008.

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34

Abtahi, Mortaza, and Sara Farhangi. "Vector-valued spectra of Banach algebra valued continuous functions." Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 112, no. 1 (December 27, 2016): 103–15. http://dx.doi.org/10.1007/s13398-016-0367-2.

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35

Zhang, Chuanyi. "Vector-valued means and weakly almost periodic functions." International Journal of Mathematics and Mathematical Sciences 17, no. 2 (1994): 227–37. http://dx.doi.org/10.1155/s0161171294000347.

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A formula is set up between vector-valued mean and scalar-valued means that enables us translate many important results about scalar-valued means developed in [1] to vector-valued means. As applications of the theory of vector-valued means, we show that the definitions of a mean in [2] and [3] are equivalent and the space of vector-valued weakly almost periodic functions is admissible.
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36

Duchoň, Miloslav, and Camille Debiève. "Moments of vector-valued functions and measures." Tatra Mountains Mathematical Publications 42, no. 1 (December 1, 2009): 199–210. http://dx.doi.org/10.2478/v10127-009-0019-4.

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Abstract There are investigated conditions under which the elements of a normed vector space are the moments of a vector-valued measure, and of a Bochner integrable function, respectively, both with values in a Banach space.
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37

ALI, TRUONG QUANG. "Fréchet vector subdifferential calculus." Carpathian Journal of Mathematics 36, no. 1 (March 1, 2020): 15–26. http://dx.doi.org/10.37193/cjm.2020.01.02.

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In this paper, we study Fréchet vector subdifferentials of vector-valued functions in normed spaces which reduceto the known ones of extended-real-valued functions. We establish relations between two kinds of Fréchet vectorsubdifferentials and between subdifferential and coderivative; some of them improve the existing relations forextended-real-valued functions. Finally, sum and chain rules among others for Fréchet subdifferentials of vector-valued functions are formulated and verified. Many examples are provided
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38

Ganiev, I. G., and O. I. Egamberdiev. "The Arens Algebras of Vector-Valued Functions." Journal of Function Spaces 2014 (2014): 1–4. http://dx.doi.org/10.1155/2014/248925.

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39

Campiti, Michele. "Korovkin-type approximation of set-valued and vector-valued functions." Mathematical Foundations of Computing 5, no. 3 (2022): 231. http://dx.doi.org/10.3934/mfc.2021032.

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<p style='text-indent:20px;'>We establish some general Korovkin-type results in cones of set-valued functions and in spaces of vector-valued functions. These results constitute a meaningful extension of the preceding ones.</p>
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40

Parthasarathy, K., and Sujatha Varma. "Wiener Tauberian theorems for vector-valued functions." International Journal of Mathematics and Mathematical Sciences 17, no. 3 (1994): 475–78. http://dx.doi.org/10.1155/s0161171294000694.

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Different versions of Wiener's Tauberian theorem are discussed for the generalized group algebraL1(G,A)(of integrable functions on a locally compact abelian groupGtaking values in a commutative semisimple regular Banach algebraA) usingA-valued Fourier transforms. A weak form of Wiener's Tauberian property is introduced and it is proved thatL1(G,A)is weakly Tauberian if and only ifAis. The vector analogue of Wiener'sL2-span of translates theorem is examined.
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41

Blasco, Oscar. "On coefficients of vector-valued Bloch functions." Studia Mathematica 165, no. 2 (2004): 101–10. http://dx.doi.org/10.4064/sm165-2-1.

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42

Spurný, Jiří. "Descriptive properties of vector-valued affine functions." Studia Mathematica 246, no. 3 (2019): 233–56. http://dx.doi.org/10.4064/sm170717-31-1.

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43

LI, Yuan-Chuan. "Invariant means on bounded vector-valued functions." Journal of the Mathematical Society of Japan 63, no. 3 (July 2011): 819–36. http://dx.doi.org/10.2969/jmsj/06330819.

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44

Álvarez, Mauricio A., Lorenzo Rosasco, and Neil D. Lawrence. "Kernels for Vector-Valued Functions: A Review." Foundations and Trends® in Machine Learning 4, no. 3 (2012): 195–266. http://dx.doi.org/10.1561/2200000036.

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45

Alomari, Mohammad W., Christophe Chesneau, and Víctor Leiva. "Grüss-Type Inequalities for Vector-Valued Functions." Mathematics 10, no. 9 (May 3, 2022): 1535. http://dx.doi.org/10.3390/math10091535.

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Grüss-type inequalities have been widely studied and applied in different contexts. In this work, we provide and prove vectorial versions of Grüss-type inequalities involving vector-valued functions defined on Rn for inner- and cross-products.
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46

Araujo, Jesus. "Realcompactness and spaces of vector-valued functions." Fundamenta Mathematicae 172, no. 1 (2002): 27–40. http://dx.doi.org/10.4064/fm172-1-3.

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47

BOUBOULIS, P., and L. DALLA. "HIDDEN VARIABLE VECTOR VALUED FRACTAL INTERPOLATION FUNCTIONS." Fractals 13, no. 03 (September 2005): 227–32. http://dx.doi.org/10.1142/s0218348x05002854.

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48

Frerick, Leonhard, and Jochen Wengenroth. "(LB)-spaces of vector-valued continuous functions." Bulletin of the London Mathematical Society 40, no. 3 (May 3, 2008): 505–15. http://dx.doi.org/10.1112/blms/bdn033.

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49

Ahlswede, R., and Ning Cai. "On communication complexity of vector-valued functions." IEEE Transactions on Information Theory 40, no. 6 (1994): 2062–67. http://dx.doi.org/10.1109/18.340481.

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50

Tammer, Christiane, and Constantin Zălinescu. "Vector variational principles for set-valued functions." Optimization 60, no. 7 (November 11, 2010): 839–57. http://dx.doi.org/10.1080/02331934.2010.522712.

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