Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators | Paper Citation Record

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This paper cites Neural operator: Graph kernel network for partial differential equations.

Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Neural operator: Graph kernel network for partial differential equations

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This paper cites Theory of reproducing kernels.Transactions of the American mathematical society, 68(3):337–404, 1950.

Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Theory of reproducing kernels.Transactions of the American mathematical society, 68(3):337–404, 1950

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This paper cites Structured sparsity-inducing norms through submodular functions.Advances in Neural Information Processing Systems, 23, 2010.

Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Structured sparsity-inducing norms through submodular functions.Advances in Neural Information Processing Systems, 23, 2010

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This paper cites Breaking the curse of dimensionality with convex neural networks.Journal of Machine Learning Research, 18(19):1–53, 2017.

Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Breaking the curse of dimensionality with convex neural networks.Journal of Machine Learning Research, 18(19):1–53, 2017

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This paper cites Iglesias, Yury Korolev, Emanuele Naldi, and Stefano Vi- gogna.

Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Iglesias, Yury Korolev, Emanuele Naldi, and Stefano Vi- gogna

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This paper cites Understanding neural networks with reproducing kernel Banach spaces.Applied and Computational Harmonic Analysis, 62:194– 236, 2023.

Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Understanding neural networks with reproducing kernel Banach spaces.Applied and Computational Harmonic Analysis, 62:194– 236, 2023

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This paper cites Neural reproducing kernel Banach spaces and representer theorems for deep networks.

Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Neural reproducing kernel Banach spaces and representer theorems for deep networks

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This paper cites Kernel methods are competitive for operator learning.Journal of Computational Physics, 496:112549, 2024.

Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Kernel methods are competitive for operator learning.Journal of Computational Physics, 496:112549, 2024

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This paper cites Kovachki, and Andrew M.

Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Kovachki, and Andrew M

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This paper cites Springer, 2007.

Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Springer, 2007

Reference 10

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This paper cites A mathematical guide to operator learning.

Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators A mathematical guide to operator learning

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This paper cites Sparsity of solutions for variational inverse problems with finite- dimensional data.Calculus of Variations and Partial Differential Equations, 59(1):14, 2020.

Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Sparsity of solutions for variational inverse problems with finite- dimensional data.Calculus of Variations and Partial Differential Equations, 59(1):14, 2020

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This paper cites Iglesias, and Daniel Walter.

Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Iglesias, and Daniel Walter

Reference 13

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This paper cites Functional learning through kernels.

Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Functional learning through kernels

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This paper cites Vector valued reproducing kernel Hilbert spaces of integrable functions and Mercer theorem.Analysis and Applications, 4(04):377–408, 2006.

Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Vector valued reproducing kernel Hilbert spaces of integrable functions and Mercer theorem.Analysis and Applications, 4(04):377–408, 2006

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This paper cites Vector valued reproducing kernel Hilbert spaces and universality.Analysis and Applications, 8(01):19–61, 2010.

Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Vector valued reproducing kernel Hilbert spaces and universality.Analysis and Applications, 8(01):19–61, 2010

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This paper cites Vector-valued Reproducing Kernel Banach Spaces with Group Lasso Norms.

Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Vector-valued Reproducing Kernel Banach Spaces with Group Lasso Norms

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This paper cites Combettes, Saverio Salzo, and Silvia Villa.

Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Combettes, Saverio Salzo, and Silvia Villa

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This paper cites Verduyn Lunel.

Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Verduyn Lunel

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This paper cites RDA-INR: Riemannian diffeomorphic autoen- coding via implicit neural representations.SIAM Journal on Imaging Sciences, 17(4):2302–2330, 2024.

Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators RDA-INR: Riemannian diffeomorphic autoen- coding via implicit neural representations.SIAM Journal on Imaging Sciences, 17(4):2302–2330, 2024

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This paper cites RONOM: Reduced-order neural operator modeling.

Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators RONOM: Reduced-order neural operator modeling

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This paper cites Springer Science & Business Media, 2011.

Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Springer Science & Business Media, 2011

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This paper cites Georgiev, Luis S´ anchez-Gonz´ alez, and Panos M.

Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Georgiev, Luis S´ anchez-Gonz´ alez, and Panos M

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This paper cites Deep Networks are Reproducing Kernel Chains.

Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Deep Networks are Reproducing Kernel Chains

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This paper cites Koopman and Perron–Frobenius operators on reproducing kernel Banach spaces.Chaos: An Interdisciplinary Journal of Nonlinear Science, 32(12), 2022.

Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Koopman and Perron–Frobenius operators on reproducing kernel Banach spaces.Chaos: An Interdisciplinary Journal of Nonlinear Science, 32(12), 2022

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This paper cites Learning in latent spaces improves the predictive accuracy of deep neural operators.

Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Learning in latent spaces improves the predictive accuracy of deep neural operators

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Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Two-layer neural networks with values in a Banach space.SIAM Journal on Mathematical Analysis, 54(6):6358–6389, 2022

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Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators On universal approximation and error bounds for fourier neural operators.Journal of Machine Learning Research, 22(290):1–76, 2021

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Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Fourier neural operator for parametric partial differential equations

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This paper cites On reproducing kernel Banach spaces: Generic definitions and unified framework of constructions.Acta Mathematica Sinica, English Series, 38(8):1459– 1483, 2022.

Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators On reproducing kernel Banach spaces: Generic definitions and unified framework of constructions.Acta Mathematica Sinica, English Series, 38(8):1459– 1483, 2022

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Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Multi-task learning in vector-valued reproducing kernel Banach spaces with theℓ 1 norm.Journal of Complexity, 63:101514, 2021

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Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators.Nature machine intelligence, 3(3):218–229, 2021

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Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators A comprehensive and fair comparison of two neural operators (with practical extensions) based on fair data.Computer Methods in Applied Mechanics and Engineering, 393:114778, 2022

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Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't

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Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators A priori estimates of the population risk for two-layer neural networks.Commu- nications in Mathematical Sciences, 17(5):1407–1425, 2019

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Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators The Barron space and the flow-induced function spaces for neural network models

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Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators On the dual spaceC ∗ 0 (S, X).Acta Math

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Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators A measure-theoretic approach to kernel conditional mean embed- dings.Advances in Neural Information Processing Systems, 33:21247–21259, 2020

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Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Paulsen and Mrinal Raghupathi.An introduction to the theory of reproducing kernel Hilbert spaces, volume 152 ofCambridge Studies in Advanced Mathematics

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Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Con- volutional neural operators

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Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Linear functionals on the space of continuous mappings of a compact Hausdorff space into a Banach space.Rev

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Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Implicit neural representations with periodic activation functions.Advances in Neural Information Processing Systems, 33:7462–7473, 2020

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Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Duality for neural networks through reproducing kernel Banach spaces.Applied and Computational Harmonic Analysis, 78:101765, 2025

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Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Reproducing kernel Hilbert spaces cannot contain all continuous functions on a compact metric space.Archiv der Mathematik, 122(5):553–557, 2024

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Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators American Mathematical Society, 2011

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Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Sparse representer theorems for learning in reproducing kernel Banach spaces.Journal of Machine Learning Research, 25(93):1–45, 2024

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Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Hypothesis spaces for deep learning.Neural Networks, 193:107995, 2026

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Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Extreme points in spaces of operators and vector-valued measures.Rend

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Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Representation formulas and pointwise properties for Barron functions.Cal- culus of Variations and Partial Differential Equations, 61(2):1–37, 2022

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Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Sparse machine learning in Banach spaces.Applied Numerical Mathematics, 187:138–157, 2023

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This paper cites Reproducing kernel Banach spaces for machine learning.

Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Reproducing kernel Banach spaces for machine learning

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This paper cites Vector-valued reproducing kernel Banach spaces with applications to multi-task learning.Journal of Complexity, 29(2):195–215, 2013.

Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators Vector-valued reproducing kernel Banach spaces with applications to multi-task learning.Journal of Complexity, 29(2):195–215, 2013

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