id sid tid token lemma pos ns064458s7j 1 1 the the DET ns064458s7j 1 2 segal segal ADJ ns064458s7j 1 3 – – PUNCT ns064458s7j 1 4 bargmann bargmann NOUN ns064458s7j 1 5 transform transform VERB ns064458s7j 1 6 on on ADP ns064458s7j 1 7 a a DET ns064458s7j 1 8 sphere sphere NOUN ns064458s7j 1 9 with with ADP ns064458s7j 1 10 a a DET ns064458s7j 1 11 positive positive ADJ ns064458s7j 1 12 time time NOUN ns064458s7j 1 13 parameter parameter NOUN ns064458s7j 1 14 is be AUX ns064458s7j 1 15 a a DET ns064458s7j 1 16 unitary unitary ADJ ns064458s7j 1 17 map map NOUN ns064458s7j 1 18 from from ADP ns064458s7j 1 19 the the DET ns064458s7j 1 20 hilbert hilbert PROPN ns064458s7j 1 21 space space NOUN ns064458s7j 1 22 of of ADP ns064458s7j 1 23 square square ADJ ns064458s7j 1 24 - - PUNCT ns064458s7j 1 25 integrable integrable ADJ ns064458s7j 1 26 functions function NOUN ns064458s7j 1 27 on on ADP ns064458s7j 1 28 the the DET ns064458s7j 1 29 sphere sphere NOUN ns064458s7j 1 30 with with ADP ns064458s7j 1 31 respect respect NOUN ns064458s7j 1 32 to to ADP ns064458s7j 1 33 its its PRON ns064458s7j 1 34 volume volume NOUN ns064458s7j 1 35 measure measure NOUN ns064458s7j 1 36 onto onto ADP ns064458s7j 1 37 the the DET ns064458s7j 1 38 hilbert hilbert PROPN ns064458s7j 1 39 space space NOUN ns064458s7j 1 40 of of ADP ns064458s7j 1 41 holomorphic holomorphic ADJ ns064458s7j 1 42 square square ADJ ns064458s7j 1 43 - - PUNCT ns064458s7j 1 44 integrable integrable ADJ ns064458s7j 1 45 functions function NOUN ns064458s7j 1 46 with with ADP ns064458s7j 1 47 respect respect NOUN ns064458s7j 1 48 to to ADP ns064458s7j 1 49 a a DET ns064458s7j 1 50 certain certain ADJ ns064458s7j 1 51 heat heat NOUN ns064458s7j 1 52 - - PUNCT ns064458s7j 1 53 kernel kernel NOUN ns064458s7j 1 54 measure measure NOUN ns064458s7j 1 55 on on ADP ns064458s7j 1 56 the the DET ns064458s7j 1 57 quadric quadric ADJ ns064458s7j 1 58 corresponding corresponding NOUN ns064458s7j 1 59 to to ADP ns064458s7j 1 60 the the DET ns064458s7j 1 61 sphere sphere NOUN ns064458s7j 1 62 . . PUNCT ns064458s7j 2 1 in in ADP ns064458s7j 2 2 this this DET ns064458s7j 2 3 thesis thesis NOUN ns064458s7j 2 4 , , PUNCT ns064458s7j 2 5 i i PRON ns064458s7j 2 6 study study VERB ns064458s7j 2 7 the the DET ns064458s7j 2 8 limiting limit VERB ns064458s7j 2 9 behavior behavior NOUN ns064458s7j 2 10 of of ADP ns064458s7j 2 11 the the DET ns064458s7j 2 12 segal segal ADJ ns064458s7j 2 13 – – PUNCT ns064458s7j 2 14 bargmann bargmann NOUN ns064458s7j 2 15 transforms transform VERB ns064458s7j 2 16 on on ADP ns064458s7j 2 17 high high ADJ ns064458s7j 2 18 dimensional dimensional ADJ ns064458s7j 2 19 spheres sphere NOUN ns064458s7j 2 20 . . PUNCT ns064458s7j 3 1 as as SCONJ ns064458s7j 3 2 the the DET ns064458s7j 3 3 dimension dimension NOUN ns064458s7j 3 4 of of ADP ns064458s7j 3 5 a a DET ns064458s7j 3 6 sphere sphere NOUN ns064458s7j 3 7 tends tend VERB ns064458s7j 3 8 to to PART ns064458s7j 3 9 infinity infinity VERB ns064458s7j 3 10 , , PUNCT ns064458s7j 3 11 with with ADP ns064458s7j 3 12 a a DET ns064458s7j 3 13 proper proper ADJ ns064458s7j 3 14 scaling scaling NOUN ns064458s7j 3 15 of of ADP ns064458s7j 3 16 its its PRON ns064458s7j 3 17 radius radius NOUN ns064458s7j 3 18 , , PUNCT ns064458s7j 3 19 the the DET ns064458s7j 3 20 normalized normalize VERB ns064458s7j 3 21 spherical spherical ADJ ns064458s7j 3 22 volume volume NOUN ns064458s7j 3 23 measure measure VERB ns064458s7j 3 24 converges converge NOUN ns064458s7j 3 25 to to ADP ns064458s7j 3 26 the the DET ns064458s7j 3 27 infinite infinite ADJ ns064458s7j 3 28 - - PUNCT ns064458s7j 3 29 dimensional dimensional ADJ ns064458s7j 3 30 unit unit NOUN ns064458s7j 3 31 - - PUNCT ns064458s7j 3 32 time time NOUN ns064458s7j 3 33 gaussian gaussian ADJ ns064458s7j 3 34 measure measure NOUN ns064458s7j 3 35 ; ; PUNCT ns064458s7j 3 36 the the DET ns064458s7j 3 37 heat heat NOUN ns064458s7j 3 38 - - PUNCT ns064458s7j 3 39 kernel kernel NOUN ns064458s7j 3 40 measure measure NOUN ns064458s7j 3 41 on on ADP ns064458s7j 3 42 the the DET ns064458s7j 3 43 quadric quadric ADJ ns064458s7j 3 44 likewise likewise ADV ns064458s7j 3 45 converges converge VERB ns064458s7j 3 46 to to ADP ns064458s7j 3 47 a a DET ns064458s7j 3 48 certain certain ADJ ns064458s7j 3 49 gaussian gaussian ADJ ns064458s7j 3 50 measure measure NOUN ns064458s7j 3 51 determined determine VERB ns064458s7j 3 52 by by ADP ns064458s7j 3 53 the the DET ns064458s7j 3 54 time time NOUN ns064458s7j 3 55 parameter parameter NOUN ns064458s7j 3 56 ; ; PUNCT ns064458s7j 3 57 and and CCONJ ns064458s7j 3 58 , , PUNCT ns064458s7j 3 59 the the DET ns064458s7j 3 60 segal segal ADJ ns064458s7j 3 61 -- -- PUNCT ns064458s7j 3 62 bargmann bargmann NOUN ns064458s7j 3 63 transform transform NOUN ns064458s7j 3 64 tends tend VERB ns064458s7j 3 65 to to ADP ns064458s7j 3 66 an an DET ns064458s7j 3 67 exponential exponential ADJ ns064458s7j 3 68 operator operator NOUN ns064458s7j 3 69 defined define VERB ns064458s7j 3 70 via via ADP ns064458s7j 3 71 the the DET ns064458s7j 3 72 hermite hermite PROPN ns064458s7j 3 73 differential differential ADJ ns064458s7j 3 74 operator operator NOUN ns064458s7j 3 75 . . PUNCT ns064458s7j 4 1 this this DET ns064458s7j 4 2 thesis thesis NOUN ns064458s7j 4 3 aims aim VERB ns064458s7j 4 4 to to PART ns064458s7j 4 5 provide provide VERB ns064458s7j 4 6 an an DET ns064458s7j 4 7 explicit explicit ADJ ns064458s7j 4 8 formulation formulation NOUN ns064458s7j 4 9 and and CCONJ ns064458s7j 4 10 describe describe VERB ns064458s7j 4 11 the the DET ns064458s7j 4 12 geometric geometric ADJ ns064458s7j 4 13 models model NOUN ns064458s7j 4 14 for for ADP ns064458s7j 4 15 these these DET ns064458s7j 4 16 convergence convergence NOUN ns064458s7j 4 17 phenomena phenomena NOUN ns064458s7j 4 18 . . PUNCT ns064458s7j 5 1 it it PRON ns064458s7j 5 2 turns turn VERB ns064458s7j 5 3 out out ADP ns064458s7j 5 4 that that SCONJ ns064458s7j 5 5 the the DET ns064458s7j 5 6 limiting limiting NOUN ns064458s7j 5 7 transform transform NOUN ns064458s7j 5 8 is be AUX ns064458s7j 5 9 still still ADV ns064458s7j 5 10 a a DET ns064458s7j 5 11 unitary unitary ADJ ns064458s7j 5 12 map map NOUN ns064458s7j 5 13 from from ADP ns064458s7j 5 14 the the DET ns064458s7j 5 15 limiting limit VERB ns064458s7j 5 16 domain domain NOUN ns064458s7j 5 17 hilbert hilbert NOUN ns064458s7j 5 18 space space NOUN ns064458s7j 5 19 onto onto ADP ns064458s7j 5 20 the the DET ns064458s7j 5 21 limiting limit VERB ns064458s7j 5 22 range range NOUN ns064458s7j 5 23 hilbert hilbert NOUN ns064458s7j 5 24 space space NOUN ns064458s7j 5 25 . . PUNCT