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Paper Abstract and Keywords
Presentation 2024-02-29 17:00
Kernel-Induced Sampling Theorem for A Class of Mapping-Prescribed Reproducing Kernel Hilbert Spaces
Akira Tanaka (Hokkaido Univ.) EA2023-79 SIP2023-126 SP2023-61
Abstract (in Japanese) (See Japanese page) 
(in English) A reproducing kernel is often interpreted as an inner product of two input vectors mapped into a certain space. On the contrary, if a mapping and a metric of the range
space of the mapping are specified, the corresponding reproducing kernel and the unique corresponding reproducing kernel Hilbert space are automatically specified. In this paper, we introduce a class of reproducing kernel Hilbert spaces prescribed by an arbitrarily fixed mapping, and discuss properties of the spaces. Moreover, we give a necessary and sufficient condition that leads the sampling theorem (perfect reconstruction of a function from sampling points) for a reproducing kernel Hilbert space in the class. In addition, we theoretically analyze the role of a metric, by which one reproducing kernel Hilbert space among the class is specified, of the class in the function reconstruction process.
Keyword (in Japanese) (See Japanese page) 
(in English) reproducing kernel / mapping / metric / kernel-induced sampling theorem / / / /  
Reference Info. IEICE Tech. Rep., vol. 123, no. 402, SIP2023-126, pp. 109-114, Feb. 2024.
Paper # SIP2023-126 
Date of Issue 2024-02-22 (EA, SIP, SP) 
ISSN Online edition: ISSN 2432-6380
Copyright
and
reproduction		 All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
Download PDF EA2023-79 SIP2023-126 SP2023-61

Conference Information
Committee SIP SP EA IPSJ-SLP  
Conference Date 2024-02-29 - 2024-03-01 
Place (in Japanese) (See Japanese page) 
Place (in English)  
Topics (in Japanese) (See Japanese page) 
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Paper Information
Registration To SIP 
Conference Code 2024-02-SIP-SP-EA-SLP 
Language English 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Kernel-Induced Sampling Theorem for A Class of Mapping-Prescribed Reproducing Kernel Hilbert Spaces 
Sub Title (in English)  
Keyword(1) reproducing kernel  
Keyword(2) mapping  
Keyword(3) metric  
Keyword(4) kernel-induced sampling theorem  
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1st Author's Name Akira Tanaka  
1st Author's Affiliation Hokkaido University (Hokkaido Univ.)
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Speaker Author-1 
Date Time 2024-02-29 17:00:00 
Presentation Time 20 minutes 
Registration for SIP 
Paper # EA2023-79, SIP2023-126, SP2023-61 
Volume (vol) vol.123 
Number (no) no.401(EA), no.402(SIP), no.403(SP) 
Page pp.109-114 
#Pages 6 
Date of Issue 2024-02-22 (EA, SIP, SP) 

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