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Journal articles on the topic 'Kernel Hilbert Spaces'

Author: Grafiati

Published: 6 September 2023

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1

Ferrer, Osmin, Diego Carrillo, and Arnaldo De La Barrera. "Reproducing Kernel in Krein Spaces." WSEAS TRANSACTIONS ON MATHEMATICS 21 (January 11, 2022): 23–30. http://dx.doi.org/10.37394/23206.2022.21.4.

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This article describes a new form to introduce a reproducing kernel for a Krein space based on orthogonal projectors enabling to describe the kernel of a Krein space as the difference between the kernel of definite positive subspace and the kernel of definite negative subspace corresponding to kernel of the associated Hilbert space. As application, the authors obtain some basic properties of both kernels for Krein spaces and exhibit that each kernel is uniquely determined by the Krein space given. The methods and results employed generalize the notion of reproducing kernel given in Hilbert spaces to the context of spaces endowed with indefinite metric.

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2

Thirulogasanthar, K., and S. Twareque Ali. "General construction of reproducing kernels on a quaternionic Hilbert space." Reviews in Mathematical Physics 29, no. 05 (May 2, 2017): 1750017. http://dx.doi.org/10.1142/s0129055x17500179.

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A general theory of reproducing kernels and reproducing kernel Hilbert spaces on a right quaternionic Hilbert space is presented. Positive operator-valued measures and their connection to a class of generalized quaternionic coherent states are examined. A Naimark type extension theorem associated with the positive operator-valued measures is proved in a right quaternionic Hilbert space. As illustrative examples, real, complex and quaternionic reproducing kernels and reproducing kernel Hilbert spaces arising from Hermite and Laguerre polynomials are presented. In particular, in the Laguerre case, the Naimark type extension theorem on the associated quaternionic Hilbert space is indicated.

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3

Ferreira, J. C., and V. A. Menegatto. "Reproducing kernel Hilbert spaces associated with kernels on topological spaces." Functional Analysis and Its Applications 46, no. 2 (April 2012): 152–54. http://dx.doi.org/10.1007/s10688-012-0021-5.

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4

Scovel, Clint, Don Hush, Ingo Steinwart, and James Theiler. "Radial kernels and their reproducing kernel Hilbert spaces." Journal of Complexity 26, no. 6 (December 2010): 641–60. http://dx.doi.org/10.1016/j.jco.2010.03.002.

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5

Kumari, Rani, Jaydeb Sarkar, Srijan Sarkar, and Dan Timotin. "Factorizations of Kernels and Reproducing Kernel Hilbert Spaces." Integral Equations and Operator Theory 87, no. 2 (February 2017): 225–44. http://dx.doi.org/10.1007/s00020-017-2348-z.

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6

CARMELI, C., E. DE VITO, A. TOIGO, and V. UMANITÀ. "VECTOR VALUED REPRODUCING KERNEL HILBERT SPACES AND UNIVERSALITY." Analysis and Applications 08, no. 01 (January 2010): 19–61. http://dx.doi.org/10.1142/s0219530510001503.

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This paper is devoted to the study of vector valued reproducing kernel Hilbert spaces. We focus on two aspects: vector valued feature maps and universal kernels. In particular, we characterize the structure of translation invariant kernels on abelian groups and we relate it to the universality problem.

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7

Ball, Joseph A., Gregory Marx, and Victor Vinnikov. "Noncommutative reproducing kernel Hilbert spaces." Journal of Functional Analysis 271, no. 7 (October 2016): 1844–920. http://dx.doi.org/10.1016/j.jfa.2016.06.010.

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8

Alpay, Daniel, Palle Jorgensen, and Dan Volok. "Relative reproducing kernel Hilbert spaces." Proceedings of the American Mathematical Society 142, no. 11 (July 17, 2014): 3889–95. http://dx.doi.org/10.1090/s0002-9939-2014-12121-6.

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9

ZHANG, HAIZHANG, and LIANG ZHAO. "ON THE INCLUSION RELATION OF REPRODUCING KERNEL HILBERT SPACES." Analysis and Applications 11, no. 02 (March 2013): 1350014. http://dx.doi.org/10.1142/s0219530513500140.

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To help understand various reproducing kernels used in applied sciences, we investigate the inclusion relation of two reproducing kernel Hilbert spaces. Characterizations in terms of feature maps of the corresponding reproducing kernels are established. A full table of inclusion relations among widely-used translation invariant kernels is given. Concrete examples for Hilbert–Schmidt kernels are presented as well. We also discuss the preservation of such a relation under various operations of reproducing kernels. Finally, we briefly discuss the special inclusion with a norm equivalence.

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10

Agud, L., J. M. Calabuig, and E. A. Sánchez Pérez. "Weighted p-regular kernels for reproducing kernel Hilbert spaces and Mercer Theorem." Analysis and Applications 18, no. 03 (October 31, 2019): 359–83. http://dx.doi.org/10.1142/s0219530519500179.

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Let [Formula: see text] be a finite measure space and consider a Banach function space [Formula: see text]. Motivated by some previous papers and current applications, we provide a general framework for representing reproducing kernel Hilbert spaces as subsets of Köthe–Bochner (vector-valued) function spaces. We analyze operator-valued kernels [Formula: see text] that define integration maps [Formula: see text] between Köthe–Bochner spaces of Hilbert-valued functions [Formula: see text] We show a reduction procedure which allows to find a factorization of the corresponding kernel operator through weighted Bochner spaces [Formula: see text] and [Formula: see text] — where [Formula: see text] — under the assumption of [Formula: see text]-concavity of [Formula: see text] Equivalently, a new kernel obtained by multiplying [Formula: see text] by scalar functions can be given in such a way that the kernel operator is defined from [Formula: see text] to [Formula: see text] in a natural way. As an application, we prove a new version of Mercer Theorem for matrix-valued weighted kernels.

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11

Karvonen, Toni, Chris Oates, and Mark Girolami. "Integration in reproducing kernel Hilbert spaces of Gaussian kernels." Mathematics of Computation 90, no. 331 (June 18, 2021): 2209–33. http://dx.doi.org/10.1090/mcom/3659.

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The Gaussian kernel plays a central role in machine learning, uncertainty quantification and scattered data approximation, but has received relatively little attention from a numerical analysis standpoint. The basic problem of finding an algorithm for efficient numerical integration of functions reproduced by Gaussian kernels has not been fully solved. In this article we construct two classes of algorithms that use N N evaluations to integrate d d -variate functions reproduced by Gaussian kernels and prove the exponential or super-algebraic decay of their worst-case errors. In contrast to earlier work, no constraints are placed on the length-scale parameter of the Gaussian kernel. The first class of algorithms is obtained via an appropriate scaling of the classical Gauss–Hermite rules. For these algorithms we derive lower and upper bounds on the worst-case error of the forms exp ⁡ ( − c 1 N 1 / d ) N 1 / ( 4 d ) \exp (-c_1 N^{1/d}) N^{1/(4d)} and exp ⁡ ( − c 2 N 1 / d ) N − 1 / ( 4 d ) \exp (-c_2 N^{1/d}) N^{-1/(4d)} , respectively, for positive constants c 1 > c 2 c_1 > c_2 . The second class of algorithms we construct is more flexible and uses worst-case optimal weights for points that may be taken as a nested sequence. For these algorithms we derive upper bounds of the form exp ⁡ ( − c 3 N 1 / ( 2 d ) ) \exp (-c_3 N^{1/(2d)}) for a positive constant c 3 c_3 .

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12

Luor, Dah-Chin, and Liang-Yu Hsieh. "Reproducing Kernel Hilbert Spaces of Smooth Fractal Interpolation Functions." Fractal and Fractional 7, no. 5 (April 27, 2023): 357. http://dx.doi.org/10.3390/fractalfract7050357.

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The theory of reproducing kernel Hilbert spaces (RKHSs) has been developed into a powerful tool in mathematics and has lots of applications in many fields, especially in kernel machine learning. Fractal theory provides new technologies for making complicated curves and fitting experimental data. Recently, combinations of fractal interpolation functions (FIFs) and methods of curve estimations have attracted the attention of researchers. We are interested in the study of connections between FIFs and RKHSs. The aim is to develop the concept of smooth fractal-type reproducing kernels and RKHSs of smooth FIFs. In this paper, a linear space of smooth FIFs is considered. A condition for a given finite set of smooth FIFs to be linearly independent is established. For such a given set, we build a fractal-type positive semi-definite kernel and show that the span of these linearly independent smooth FIFs is the corresponding RKHS. The nth derivatives of these FIFs are investigated, and properties of related positive semi-definite kernels and the corresponding RKHS are studied. We also introduce subspaces of these RKHS which are important in curve-fitting applications.

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13

Hashemi Sababe, Saeed, Ali Ebadian, and Shahram Najafzadeh. "On reproducing property and 2-cocycles." Tamkang Journal of Mathematics 49, no. 2 (June 30, 2018): 143–53. http://dx.doi.org/10.5556/j.tkjm.49.2018.2553.

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In this paper, we study reproducing kernels whose ranges are subsets of a $C^*$-algebra or a Hilbert $C^*$-module. In particular, we show how such a reproducing kernel can naturally be expressed in terms of operators on a Hilbert $C^*$-module. We focus on relative reproducing kernels and extend this concept to such spaces associated with cocycles.

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14

Alpay, Daniel, and Palle E. T. Jorgensen. "New characterizations of reproducing kernel Hilbert spaces and applications to metric geometry." Opuscula Mathematica 41, no. 3 (2021): 283–300. http://dx.doi.org/10.7494/opmath.2021.41.3.283.

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We give two new global and algorithmic constructions of the reproducing kernel Hilbert space associated to a positive definite kernel. We further present a general positive definite kernel setting using bilinear forms, and we provide new examples. Our results cover the case of measurable positive definite kernels, and we give applications to both stochastic analysis and metric geometry and provide a number of examples.

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15

Xu, Lixiang, Bin Luo, Yuanyan Tang, and Xiaohua Ma. "An efficient multiple kernel learning in reproducing kernel Hilbert spaces (RKHS)." International Journal of Wavelets, Multiresolution and Information Processing 13, no. 02 (March 2015): 1550008. http://dx.doi.org/10.1142/s0219691315500083.

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The reproducing kernel Hilbert space construction is a bijection or transform theory which associates a positive definite kernel with a Hilbert space of functions. Recently, reproducing kernel Hilbert space (RKHS) has come wildly alive in the pattern recognition and machine learning community. In this paper, we propose a novel method named multiple kernel learning with reproducing property (MKLRP) to achieve some classification tasks. The MKLRP consists of two major steps. First, we find the basic solution of a generalized differential operator by delta function, and prove this basic solution is a new specific reproducing kernel called H2-reproducing kernel (HRK) in RKHS. Second, in RKHS, we prove that the HRK satisfies the condition of Mercer kernel. Furthermore, a novel specific multiple kernel learning (MKL) called MKLRP, which is based on reproducing kernel is proposed. We perform an extensive experimental evaluation on synthetic and real-world data, which shows the effectiveness of the proposed approach.

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16

Krejnik, M., and A. Tyutin. "Reproducing Kernel Hilbert Spaces With Odd Kernels in Price Prediction." IEEE Transactions on Neural Networks and Learning Systems 23, no. 10 (October 2012): 1564–73. http://dx.doi.org/10.1109/tnnls.2012.2207739.

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17

Zhuravlov, V., N. Gongalo, and I. Slusarenko. "CONTROLLABILITY OF FREDHOLM’S INTEGRO-DIFFERENTIAL EQUATIONS WITH BY A DEGENERATE KERNEL IN HILBERT SPACES." Bukovinian Mathematical Journal 10, no. 1 (2022): 51–60. http://dx.doi.org/10.31861/bmj2022.01.05.

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The work examines integro-diﬀerential equations Fredholm with a degenerate kernel with Hilbert control spaces. The need to study these equations is related to numerous ones applications of integro- diﬀerential equations in mathematics, physics, technology, economy and other ﬁelds. Complexity the study of integro-diﬀerential equations is connected with the fact that the integral-diﬀerential operator is not solvable everywhere. There are diﬀerent approaches to the solution of not everywhere solvable linear operator equations: weak perturbation of the right-hand side of this equation with further application of the Vishyk-Lyusternyk method, introduction to system of impulse action, control, etc. The problem of obtaining coeﬃcient conditions of solvability and analytical presentation of general solutions of integro-diﬀerential equations is a rather diﬃcult problem, so frequent solutions will suﬃce are obtained by numerical methods. In this connection, Fredholm’s integro-diﬀerential equations with degenerate kernel and control in Hilbert spaces no were investigated. Therefore, the task of establishing conditions is urgent controllability, construction of general solutions in an analytical form and corresponding general controls of integro-diﬀerential equations with a degenerate kernel in abstract Hilbert spaces. As an intermediate result in the work using the results of pseudoinversion of integral operators in Hilbert spaces the solvability criterion and the form of general solutions are established integro-diﬀerential equations without control in the abstract Hilbert spaces. To establish the controllability criterion is not solvable everywhere integro-diﬀerential equations with Hilbert control spaces, the general theory of research is not applied everywhere solvable operator equations. At the same time, they are used signiﬁcantly orthoprojectors, pseudo-inverse operators to normally solvable ones operators in Hilbert spaces. With the use of orthoprojectors, pseudo-inverse operators and pseudoinversion of integraloperators, a criterion is obtained solutions and the general form of solutions of integro-diﬀerential equations with a degenerate kernel with control y Hilbert spaces. An image of the general appearance is obtained control under which these solutions exist.

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18

Manton, Jonathan H., and Pierre-Olivier Amblard. "A Primer on Reproducing Kernel Hilbert Spaces." Foundations and Trends® in Signal Processing 8, no. 1-2 (2015): 1–126. http://dx.doi.org/10.1561/2000000050.

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19

YAMANCİ, Ulas. "Operator inequalities in reproducing kernel Hilbert spaces." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 71, no. 1 (March 31, 2022): 204–11. http://dx.doi.org/10.31801/cfsuasmas.926981.

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20

Agbokou, Komi, and Yaogan Mensah. "INFERENCE ON THE REPRODUCING KERNEL HILBERT SPACES." Universal Journal of Mathematics and Mathematical Sciences 15 (October 10, 2021): 11–29. http://dx.doi.org/10.17654/2277141722002.

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21

Li, Youjuan, Yufeng Liu, and Ji Zhu. "Quantile Regression in Reproducing Kernel Hilbert Spaces." Journal of the American Statistical Association 102, no. 477 (March 2007): 255–68. http://dx.doi.org/10.1198/016214506000000979.

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22

Nhan, Nguyen Du Vi, and Dinh Thanh Duc. "VARIOUS INEQUALITIES IN REPRODUCING KERNEL HILBERT SPACES." Taiwanese Journal of Mathematics 17, no. 1 (January 2013): 221–37. http://dx.doi.org/10.11650/tjm.17.2013.2133.

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23

Napalkov, V. V., and V. V. Napalkov. "On isomorphism of reproducing kernel Hilbert spaces." Doklady Mathematics 95, no. 3 (May 2017): 270–72. http://dx.doi.org/10.1134/s1064562417030243.

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24

Dubi, Chen, and Harry Dym. "Riccati inequalities and reproducing kernel Hilbert spaces." Linear Algebra and its Applications 420, no. 2-3 (January 2007): 458–82. http://dx.doi.org/10.1016/j.laa.2006.08.005.

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25

Bouboulis, P., and M. Mavroforakis. "Reproducing Kernel Hilbert Spaces and fractal interpolation." Journal of Computational and Applied Mathematics 235, no. 12 (April 2011): 3425–34. http://dx.doi.org/10.1016/j.cam.2011.02.003.

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26

Martin, R. T. W. "Symmetric Operators and Reproducing Kernel Hilbert Spaces." Complex Analysis and Operator Theory 4, no. 4 (April 17, 2009): 845–80. http://dx.doi.org/10.1007/s11785-009-0017-1.

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27

Mundayadan, Aneesh, and Jaydeb Sarkar. "Linear dynamics in reproducing kernel Hilbert spaces." Bulletin des Sciences Mathématiques 159 (March 2020): 102826. http://dx.doi.org/10.1016/j.bulsci.2019.102826.

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28

Schroeck, F. E. "Quantum fields for reproducing kernel Hilbert spaces." Reports on Mathematical Physics 26, no. 2 (October 1988): 197–210. http://dx.doi.org/10.1016/0034-4877(88)90023-7.

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29

Das, Suddhasattwa, and Dimitrios Giannakis. "Koopman spectra in reproducing kernel Hilbert spaces." Applied and Computational Harmonic Analysis 49, no. 2 (September 2020): 573–607. http://dx.doi.org/10.1016/j.acha.2020.05.008.

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30

Li, Xian-Jin. "On Reproducing Kernel Hilbert Spaces of Polynomials." Mathematische Nachrichten 185, no. 1 (February 6, 2009): 115–48. http://dx.doi.org/10.1002/mana.3211850110.

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31

El-Sabbagh, A. A. "On the expansion theorem described byH(A,B)spaces." International Journal of Mathematics and Mathematical Sciences 2004, no. 32 (2004): 1703–14. http://dx.doi.org/10.1155/s0161171204007392.

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The aim of this paper is to construct a generalized Fourier analysis for certain Hermitian operators. WhenA,Bare entire functions, thenH(A,B)will be the associated reproducing kernel Hilbert spaces ofℂn×n-valued functions. In that case, we will construct the expansion theorem forH(A,B)in a comprehensive manner. The spectral functions for the reproducing kernel Hilbert spaces will also be constructed.

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32

Sun, Hong-Wei, and Ding-Xuan Zhou. "Reproducing Kernel Hilbert Spaces Associated with Analytic Translation-Invariant Mercer Kernels." Journal of Fourier Analysis and Applications 14, no. 1 (January 24, 2008): 89–101. http://dx.doi.org/10.1007/s00041-007-9003-z.

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33

CHEN, HENG, and JITAO WU. "KERNEL METHODS FOR INDEPENDENCE MEASUREMENT WITH COEFFICIENT CONSTRAINTS." International Journal of Wavelets, Multiresolution and Information Processing 12, no. 01 (December 2013): 1450006. http://dx.doi.org/10.1142/s0219691314500064.

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Tests to determine the dependence or independence of random variables X and Y are well established. Recently, criteria based on reproducing kernel Hilbert spaces has received much attentions. They are developed in the setting of norm of Hilbert spaces. In this paper we propose tests in the setting of constraints of coefficients of functions. Some estimates of tests are constructed. In particular the error between the test of constrained covariance and the estimate is bounded.

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34

Hartz, Michael. "On the Isomorphism Problem for Multiplier Algebras of Nevanlinna-Pick Spaces." Canadian Journal of Mathematics 69, no. 1 (February 1, 2017): 54–106. http://dx.doi.org/10.4153/cjm-2015-050-6.

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AbstractWe continue the investigation of the isomorphism problem for multiplier algebras of reproducing kernel Hilbert spaces with the complete Nevanlinna-Pick property. In contrast to previous work in this area, we do not study these spaces by identifying them with the restrictions of a universal space, namely theDrury-Arveson space. Instead, we work directly with theHilbert spaces and their reproducing kernels. In particular, we show that two multiplier algebras of Nevanlinna-Pick spaces on the same set are equal if and only if the Hilbert spaces are equal. Most of the article is devoted to the study of a special class of complete Nevanlinna-Pick spaces on homogeneous varieties. We provide a complete answer to the question of when two multiplier algebras of spaces of this type are algebraically or isometrically isomorphic.This generalizes results of Davidson, Ramsey,Shalit, and the author.

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35

Astala, Kari, Lassi Päivärinta, and Eero Saksman. "The finite Hilbert transform in weighted spaces." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 126, no. 6 (1996): 1157–67. http://dx.doi.org/10.1017/s0308210500023337.

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The mapping properties of the finite Hilbert-transform (respectively the Hilbert transform on the half axis) are studied. Invertibility, surjectivity, injectivity and bounded ness from below of the transform are characterised in general weighted spaces. The results are applied to the restriction of the operator with logarithmic kernel.

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36

Barbieri, D., and G. Citti. "Reproducing kernel Hilbert spaces of CR functions for the Euclidean motion group." Analysis and Applications 13, no. 03 (March 5, 2015): 331–46. http://dx.doi.org/10.1142/s021953051450047x.

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We study the geometric structure of the reproducing kernel Hilbert space associated to the continuous wavelet transform generated by the irreducible representations of the group of Euclidean motions of the plane SE(2). A natural Hilbert norm for functions on the group is constructed that makes the wavelet transform an isometry, but since the considered representations are not square integrable, the resulting Hilbert space will not coincide with L2( SE (2)). The reproducing kernel Hilbert subspace generated by the wavelet transform, for the case of a minimal uncertainty mother wavelet, can be characterized in terms of the complex regularity defined by the natural CR structure of the group. Relations with the Bargmann transform are presented.

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37

Ferreira, J‎ ‎C‎, and V‎ ‎A‎ Menegatto. "Positive definiteness‎, ‎reproducing kernel Hilbert spaces and beyond." Annals of Functional Analysis 4, no. 1 (2013): 64–88. http://dx.doi.org/10.15352/afa/1399899838.

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38

Gori, Franco, and Rosario Martínez-Herrero. "Reproducing Kernel Hilbert spaces for wave optics: tutorial." Journal of the Optical Society of America A 38, no. 5 (April 26, 2021): 737. http://dx.doi.org/10.1364/josaa.422738.

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39

Speckbacher, Michael, and Peter Balazs. "Frames, their relatives and reproducing kernel Hilbert spaces." Journal of Physics A: Mathematical and Theoretical 53, no. 1 (December 10, 2019): 015204. http://dx.doi.org/10.1088/1751-8121/ab573c.

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40

Lata, Sneh, and Vern I. Paulsen. "The Feichtinger Conjecture and Reproducing Kernel Hilbert Spaces." Indiana University Mathematics Journal 60, no. 4 (2011): 1303–18. http://dx.doi.org/10.1512/iumj.2011.60.4358.

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41

Bolotnikov, Vladimir. "Interpolation for multipliers on reproducing kernel Hilbert spaces." Proceedings of the American Mathematical Society 131, no. 5 (December 6, 2002): 1373–83. http://dx.doi.org/10.1090/s0002-9939-02-06899-5.

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42

Yang, Yi, Teng Zhang, and Hui Zou. "Flexible Expectile Regression in Reproducing Kernel Hilbert Spaces." Technometrics 60, no. 1 (June 19, 2017): 26–35. http://dx.doi.org/10.1080/00401706.2017.1291450.

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43

Kühn, Thomas. "Covering numbers of Gaussian reproducing kernel Hilbert spaces." Journal of Complexity 27, no. 5 (October 2011): 489–99. http://dx.doi.org/10.1016/j.jco.2011.01.005.

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44

Wang, Rui, and Haizhang Zhang. "Optimal sampling points in reproducing kernel Hilbert spaces." Journal of Complexity 34 (June 2016): 129–51. http://dx.doi.org/10.1016/j.jco.2015.11.010.

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45

Richardson, Casey L., and Laurent Younes. "Metamorphosis of images in reproducing kernel Hilbert spaces." Advances in Computational Mathematics 42, no. 3 (October 21, 2015): 573–603. http://dx.doi.org/10.1007/s10444-015-9435-y.

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46

Watanabe, Shigeru. "Jacobi polynomials and associated reproducing kernel Hilbert spaces." Journal of Mathematical Analysis and Applications 389, no. 1 (May 2012): 108–18. http://dx.doi.org/10.1016/j.jmaa.2011.11.056.

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47

Moore, R. L., and T. T. Trent. "Factoring positive operators on reproducing kernel Hilbert spaces." Integral Equations and Operator Theory 24, no. 4 (December 1996): 470–83. http://dx.doi.org/10.1007/bf01191621.

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48

Chen, Zhixiang. "On approximation by spherical reproducing kernel Hilbert spaces." Analysis in Theory and Applications 23, no. 4 (December 2007): 325–33. http://dx.doi.org/10.1007/s10496-007-0325-0.

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49

Amstler, Clemens, and Peter Zinterhof. "Uniform Distribution, Discrepancy, and Reproducing Kernel Hilbert Spaces." Journal of Complexity 17, no. 3 (September 2001): 497–515. http://dx.doi.org/10.1006/jcom.2001.0580.

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50

Yamancı, Ulaş, Mehmet Gürdal, and Mubariz Garayev. "Berezin number inequality for convex function in reproducing Kernel Hilbert Space." Filomat 31, no. 18 (2017): 5711–17. http://dx.doi.org/10.2298/fil1718711y.

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By using Hardy-Hilbert?s inequality, some power inequalities for the Berezin number of a selfadjoint operators in Reproducing Kernel Hilbert Spaces (RKHSs) with applications for convex functions are given.

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