{"abstracts":[{"sha1":"c1b6b4b2d0fc9bc278d67dffde0c1e0aea7d00bb","content":"In this paper we study algebraic structures of the classes of the L_2\nanalytic Fourier-Feynman transforms on Wiener space. To do this we first\ndevelop several rotation properties of the generalized Wiener integral\nassociated with Gaussian processes. We then proceed to analyze the L_2\nanalytic Fourier-Feynman transforms associated with Gaussian processes. Our\nresults show that these L_2 analytic Fourier--Feynman transforms are actually\nlinear operator isomorphisms from a Hilbert space into itself. We finally\ninvestigate the algebraic structures of these classes of the transforms on\nWiener space, and show that they indeed are group isomorphic.","mimetype":"text/plain","lang":"en"},{"sha1":"5a033225e2432027c0a8a18bb0c7ec99b906efd5","content":"In this paper we study algebraic structures of the classes of the $L_2$\nanalytic Fourier-Feynman transforms on Wiener space. To do this we first\ndevelop several rotation properties of the generalized Wiener integral\nassociated with Gaussian processes. We then proceed to analyze the $L_2$\nanalytic Fourier-Feynman transforms associated with Gaussian processes. Our\nresults show that these $L_2$ analytic Fourier--Feynman transforms are actually\nlinear operator isomorphisms from a Hilbert space into itself. We finally\ninvestigate the algebraic structures of these classes of the transforms on\nWiener space, and show that they indeed are group isomorphic.","mimetype":"application/x-latex","lang":"en"}],"refs":[],"contribs":[{"index":0,"raw_name":"Seung Jun Chang","role":"author"},{"index":1,"raw_name":"Jae Gil Choi","role":"author"},{"index":2,"raw_name":"David Skoug","role":"author"}],"license_slug":"ARXIV-1.0","language":"en","version":"v2","ext_ids":{"arxiv":"1511.03564v2"},"release_year":2019,"release_date":"2019-04-17","release_stage":"submitted","release_type":"article","webcaptures":[],"filesets":[],"files":[{"release_ids":["z5oxtjl2nzco3ccnp3eyebwcaq"],"mimetype":"application/pdf","urls":[{"url":"https://arxiv.org/pdf/1511.03564v2.pdf","rel":"repository"},{"url":"https://web.archive.org/web/20191012225647/https://arxiv.org/pdf/1511.03564v2.pdf","rel":"webarchive"}],"sha256":"f41297fa297edefb4d8776553d60463deaa06044b7567e7b84411cd847cd4135","sha1":"b7373753278b5663d7807e917180a4bd8be26300","md5":"d0e7d3fa74e2cd05aed304185c310b45","size":223738,"revision":"34f41ba7-5aed-4e27-a850-cd07cf783ed5","ident":"y4umy2kxpfay7aylylwqb2zkga","state":"active"}],"work_id":"wgaqftibrzgnzguwce5wamczqq","title":"Algebraic structure of the L_2 analytic Fourier-Feynman transform\n associated with Gaussian processes on Wiener space","state":"active","ident":"z5oxtjl2nzco3ccnp3eyebwcaq","revision":"8c31e855-4b0e-4e7e-b571-289c5c16b21f","extra":{"arxiv":{"base_id":"1511.03564","categories":["math.PR"],"comments":"19pages"}}}