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Be among the first to hear about our newest research by following us on YouTube. https://images.squarespace-cdn.com/content/v1/5f74e7ea77f61f77cb2a98b8/1603659273322-T9GECZZ300WQFK3N588V/IMG_1089.jpg Home - About Using our background in the theory of reproducing kernels, we execute innovative approaches to the study of dynamical systems. https://images.squarespace-cdn.com/content/v1/5f74e7ea77f61f77cb2a98b8/1603659240667-11OXA7G8N1LB0ED3MAXU/docksunset.jpg Home https://www.thelearningdock.org/team daily 0.75 2020-11-11 https://images.squarespace-cdn.com/content/v1/5f74e7ea77f61f77cb2a98b8/1605120186015-QQXF4IB5Y7EUJDINC454/xiuying.jpg Team https://images.squarespace-cdn.com/content/v1/5f74e7ea77f61f77cb2a98b8/1604783135530-F5NDLSR2JFI26DU1ZLYR/efrain.jpg Team https://images.squarespace-cdn.com/content/v1/5f74e7ea77f61f77cb2a98b8/1604782782705-BW3Q4ZLLRFNIN4M4BA7C/himanshu.jpg Team https://images.squarespace-cdn.com/content/v1/5f74e7ea77f61f77cb2a98b8/1604113295525-6NLET03OL9SB6TNLQO67/joelrosenfeld-2.jpg Team Picture taken during my postdoctoral interview at Vanderbilt University. https://images.squarespace-cdn.com/content/v1/5f74e7ea77f61f77cb2a98b8/1603678166722-RLPNC98V45YUKILX9H02/IMG_3946.JPG Team https://www.thelearningdock.org/what-we-do daily 0.75 2020-10-02 https://images.squarespace-cdn.com/content/v1/5f74e7ea77f61f77cb2a98b8/1603659372271-QFZZIQ44NSNJI66PTVDK/ufl_mae.jpg What We Do https://www.thelearningdock.org/research daily 0.75 2020-10-31 https://images.squarespace-cdn.com/content/v1/5f74e7ea77f61f77cb2a98b8/1601666522939-Y088EQ7CZNE119C8E2Y8/IMG_4015.jpg Our Work https://www.thelearningdock.org/thatmaththing daily 0.75 2020-10-26 https://images.squarespace-cdn.com/content/v1/52a74d9ae4b0253945d2aee9/1390597413198-XUEB2J3138YBEXDCIMC0/tumblr_migjb4LxOB1rkz363o2_1280.jpg Th@MathThing https://www.thelearningdock.org/fractional-calculus-and-dynamical-systems daily 0.75 2020-11-26 https://images.squarespace-cdn.com/content/v1/5f74e7ea77f61f77cb2a98b8/1603676658331-QTQVEPYBY2RW197BU4CW/Screen+Shot+2020-10-25+at+9.43.57+PM.png Fractional Calculus and Dynamical Systems - Convergence Rate Estimates for the Kernelized Adams Bashforth Moulton Method for Fractional Order Initial Value Problems Joel A. Rosenfeld and Warren E. Dixon (Accepted at Fractional Calculus and Applied Analysis) https://images.squarespace-cdn.com/content/v1/5f74e7ea77f61f77cb2a98b8/1603676818980-OP03VAKEAZELZ9M9ZJ0K/Screen+Shot+2020-10-25+at+9.46.39+PM.png Fractional Calculus and Dynamical Systems - A Mesh-free Pseudospectral Approachfor Estimating the Fractional Laplacian via Radial Basis Functions Joel A. Rosenfeld, Spencer A. Rosenfeld, Warren E. Dixon https://images.squarespace-cdn.com/content/v1/5f74e7ea77f61f77cb2a98b8/1603677087788-TSVC32846BAZB14Z5TIT/Screen%2BShot%2B2020-10-25%2Bat%2B9.50.48%2BPM.jpg Fractional Calculus and Dynamical Systems - Mittag-Leffler Reproducing Kernel Hilbert Spaces of Entire and Analytic Function Joel A. Rosenfeld, Benjamin P. Russo, Warren E. Dixon https://images.squarespace-cdn.com/content/v1/5f74e7ea77f61f77cb2a98b8/1603677524123-AQ1CYO5PGLMIMH956VSP/Screen+Shot+2020-10-25+at+9.24.53+PM.png Fractional Calculus and Dynamical Systems - Fractional Order System Identification with Occupation KernelRegression Xiuying Li and Joel A. Rosenfeld (Under Review) https://images.squarespace-cdn.com/content/v1/5f74e7ea77f61f77cb2a98b8/1603677340388-9TS1OW3PDO60IQ1A4VID/Screen+Shot+2020-10-25+at+9.55.19+PM.png Fractional Calculus and Dynamical Systems - Approximating the Caputo Fractional Derivative throughthe Mittag-Leffler Reproducing Kernel Hilbert Space and the Kernelized Adams-Bashforth-Moulton Method, Joel A. Rosenfeld and Warren E. Dixon https://www.thelearningdock.org/dynamic-mode-decomposition-and-system-identification daily 0.75 2020-10-26 https://images.squarespace-cdn.com/content/v1/5f74e7ea77f61f77cb2a98b8/1603674572402-AD0KW8F4VHB12SDJQAC9/Screen%2BShot%2B2020-10-25%2Bat%2B9.07.07%2BPM.jpg Dynamic Mode Decomposition and System Identification - Theoretical Foundations for Higher Order Dynamic Mode Decompositions Joel A. Rosenfeld, Rushikesh Kamalapurkar, Benjamin P. Russo (Under Review) https://images.squarespace-cdn.com/content/v1/5f74e7ea77f61f77cb2a98b8/1603674088639-OYMWX3SVUIFU08LELCQC/Screen%252BShot%252B2020-10-25%252Bat%252B8.59.34%252BPM.jpg Dynamic Mode Decomposition and System Identification - The Occupation Kernel Method for Nonlinear System Identification Joel A. Rosenfeld, Benjamin Russo, Rushikesh Kamalapurkar, Taylor T. Johnson (Under Review) https://images.squarespace-cdn.com/content/v1/5f74e7ea77f61f77cb2a98b8/1603676195878-L1Q9OUBQH1NX6Q0UHS5Z/Screen%2BShot%2B2020-10-25%2Bat%2B9.35.00%2BPM.jpg Dynamic Mode Decomposition and System Identification - Motion Tomography via Occupation Kernels Benjamin P. Russo, Rushikesh Kamalapurkar, Dongsik Chang, Joel A. Rosenfeld (Under Review) https://images.squarespace-cdn.com/content/v1/5f74e7ea77f61f77cb2a98b8/1603675223052-Y7BZ39LYXQ4KSF3OETOR/Screen+Shot+2020-10-25+at+9.20.10+PM.png Dynamic Mode Decomposition and System Identification - Occupation Kernels and Densely Defined Liouville Operators for System Identification Joel A. Rosenfeld, Benjamin Russo, Rushikesh Kamalapurkar, Taylor T. Johnson Proceedings of Conference on Decision and Control 2019 https://images.squarespace-cdn.com/content/v1/5f74e7ea77f61f77cb2a98b8/1603674572402-AD0KW8F4VHB12SDJQAC9/Screen%2BShot%2B2020-10-25%2Bat%2B9.07.07%2BPM.jpg Dynamic Mode Decomposition and System Identification - Dynamic Mode Decomposition with Control Liouville Operators Joel A. Rosenfeld and Rushikesh Kamalapurkar (Accepted to MTNS 2021) https://images.squarespace-cdn.com/content/v1/5f74e7ea77f61f77cb2a98b8/1603674572402-AD0KW8F4VHB12SDJQAC9/Screen%2BShot%2B2020-10-25%2Bat%2B9.07.07%2BPM.jpg Dynamic Mode Decomposition and System Identification - Dynamic Mode Decomposition for Continuous Time Systems with the Liouville Operator Joel A. Rosenfeld, Rushikesh Kamalapurkar, L. Forest Gruss, Taylor T. Johnson (Under Review) https://images.squarespace-cdn.com/content/v1/5f74e7ea77f61f77cb2a98b8/1603675504210-W9HMBT5ZXZG25R4TIA35/Screen+Shot+2020-10-25+at+9.24.53+PM.png Dynamic Mode Decomposition and System Identification - Fractional Order System Identification with Occupation KernelRegression Xiuying Li, Joel A. Rosenfeld (Under Review) https://images.squarespace-cdn.com/content/v1/5f74e7ea77f61f77cb2a98b8/1603674572402-AD0KW8F4VHB12SDJQAC9/Screen%2BShot%2B2020-10-25%2Bat%2B9.07.07%2BPM.jpg Dynamic Mode Decomposition and System Identification - On Occupation Kernels, Liouville Operators, and Dynamic Mode Decomposition Joel A. Rosenfeld, Rushikesh Kamalapurkar, L. Forest Gruss, Taylor T. Johnson (Under Review) https://www.thelearningdock.org/function-theoretic-operator-theory daily 0.75 2020-11-08 https://images.squarespace-cdn.com/content/v1/5f74e7ea77f61f77cb2a98b8/1604846427172-V96P6LNIDMUKOE0ONPE7/Screen+Shot+2020-11-08+at+9.40.15+AM.png Function Theoretic Operator Theory - Introducing the Polylogarithmic Hardy Space Joel A. Rosenfeld https://images.squarespace-cdn.com/content/v1/5f74e7ea77f61f77cb2a98b8/1604846636375-9UAR9QWBQ0PTI1HKQPKP/Screen+Shot+2020-11-08+at+9.43.45+AM.png Function Theoretic Operator Theory - The Sarason sub-symbol and the recovery of the symbol of densely defined Toeplitz operators over the Hardy space Joel A. Rosenfeld https://images.squarespace-cdn.com/content/v1/5f74e7ea77f61f77cb2a98b8/1604846953805-4O0DI31OAZSRGRM60HDU/Screen+Shot+2020-11-08+at+9.48.33+AM.png Function Theoretic Operator Theory - Densely Defined Multiplication on Several Sobolev Spaces of a Single Variable Joel A. Rosenfeld https://www.thelearningdock.org/contact-1 daily 0.75 2020-10-25 https://images.squarespace-cdn.com/content/v1/52a74d9ae4b0253945d2aee9/1390510556456-TV8RZ8LOBB3L6TBXFWZD/tumblr_mkrr2pZQ851rkz363o2_1280.jpg Contact https://www.thelearningdock.org/reproducing-kernel-hilbert-spaces daily 0.75 2020-11-26 https://images.squarespace-cdn.com/content/v1/5f74e7ea77f61f77cb2a98b8/1604846427172-V96P6LNIDMUKOE0ONPE7/Screen+Shot+2020-11-08+at+9.40.15+AM.png Reproducing Kernel Hilbert Spaces - Introducing the Polylogarithmic Hardy Space Joel A. Rosenfeld https://images.squarespace-cdn.com/content/v1/5f74e7ea77f61f77cb2a98b8/1603677059934-V4N6ZA6UK91L3G817I0R/Screen+Shot+2020-10-25+at+9.50.48+PM.png Reproducing Kernel Hilbert Spaces - The Mittag Leffler reproducing kernel Hilbert spaces of entire and analytic functions Joel A. Rosenfeld, Benjamin Russo, Warren E. 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