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@ARTICLE{Jimbo1, author = {Jimbo, M. }, title = {A $q$-analogue of ${U}({\bf gl}({N}+1))$, {H}ecke algebra and the {Y}ang-{B}axter equation }, journal = {Lett. Math. Phys. }, volume = {11 }, number = {3 }, year = {1986 }, pages = {247--252 }, } @ARTICLE{adv, author = {Ostrovski\u\i{}, V. L. and Samo\u\i{}lenko, Yu. S.}, title = {Structure theorems for a pair of unbounded selfadjoint operators satisfying a quadratic relation}, journal = {Adv. Sov. Math.}, volume = {9}, year = {1992}, pages = {131--149}, } @book{ber0, author = {Berezansky, Yu. M.}, title = {Expansion in eigenfunctions of selfadjoint operators}, series = {Transl. Math. Monogr.}, volume = {17}, year = {1968}, publisher = {Amer. Math. Soc.}, address = {Providence, R.I.}, note = {Transl. from Russian edn.: Naukova Dumka, Kiev, 1965} } @BOOK{ber1, author = {Berezansky, Yu. M.}, title = {Self-adjoint operators in spaces of functions of infinitely many variables}, publisher = {AMS}, address = {Providence, R.I.}, year = 1986, series = {Trans. Math. Monographs}, volume = 63, note = {Transl. from Russian edn.: Kiev, Naukova Dumka, 1978} } @ARTICLE{berez_umn, author = {Berezansky, Yu. M. }, title = {Projection spectral theorem }, journal = {Usp. Mat. Nauk }, volume = {39 }, number = {4 }, year = {1984 }, pages = {3--52 }, } @BOOK{berkon, author = {Berezansky, Yu. M. and Kondrat'ev, Yu. G. }, title = {Spectral methods in infinite dimensional analysis }, publisher = {Kluwer Acad. Publ. }, year = {1992 }, address = {Dordrecht}, note = {Transl. from Russian edn.: Naukova Dumka, Kiev, 1988 } } @ARTICLE{besp2, author = {Bespalov, Yu. N. }, title = {On selfadjoint representations of {S}klyanin algebra }, journal = {Ukrain. Math. Zh. }, volume = {43 }, number = { }, year = {1991 }, pages = {1567--1574 }, note = {(Russian)}, } @ARTICLE{bessam1, author = {Bespalov, Yu. N. and Samo\u\i{}lenko, Yu. S. }, title = {Algebraic operators and pairs of selfadjoint operators connected by a polynomial relation }, journal = {Funct. Anal. i Prilozhen. }, volume = {25 }, number = {4 }, year = {1991 }, pages = {72--74 }, note = {(Russian)}, } @article{biede, author = {Biedenharn, L. C.}, title = {The quantum group $SU_q(2)$ and a $q$-analogue of the boson operators}, journal = {J. Phys. A}, volume = {22}, year = {1989}, pages = {L873--L878}, } @BOOK{book, author = {Samo\u\i{}lenko, Yu. S.}, title = {Spectral theory of families of self-adjoint operators}, publisher = {Kluwer Academic Publisher}, year = 1991, note = {Transl. from Russian edn.: Naukova Dumka, Kiev, 1984}, } @ARTICLE{bos, author = {Berezansky, Yu. M. and Ostrovski\u\i{}, V. L. and Samo\u\i{}lenko, Yu. S.}, title = {Eigenfunction expansion of families of commuting operators and representations of commutation relations}, journal = {Ukr. Math. Zh.}, volume = 40, number = 1, year = 1988, pages = {106--109}, note = {(Russian)} } @Article{bra_jor1, author = {Bratteli, O. and J\o{}rgensen, P. E. T. and Price, G. L.}, title = {Endomorphisms of {$\mathcal B(\mathcal H)$}}, journal = {Proc. Symp. Pure Math.}, year = 1996, volume = 59, pages = {93--138} } @Article{bra_jor2, author = {Bratteli, O. and J\o{}rgensen, P. E. T.}, title = {Endomorphisms of {$\mathcal B(\mathcal H)$}. {II}. {F}initely correlated states on {$\mathcal{O}_n$}}, journal = {J. Funct. Anal.}, year = 1997, volume = 145, number = 2, pages = {323--373} } @book{brat-jorg, author = {O. Bratteli and P. E.~T. J\o{}rgensen}, title = {Iterated function systems and permutation representations of the {C}untz algebra}, year = {1998}, series = {Mem. Amer. Math. Soc.}, publisher = {AMS} } @INCOLLECTION{bss, author = {Bespalov, Yu. N. and Samo\u\i{}lenko, Yu. S. and Shul'man, V. S. }, title = {On families of operators connected by semi-linear relations }, booktitle = {Applications of Methods of Functional Analysis in Mathematical Physics }, publisher = {Inst. Math. Acad. Sci. Ukraine, Kiev }, year = {1991 }, pages = {28--51 }, note = {(Russian) } } @ARTICLE{bukl, author = {Burban, I. M. and Klimyk, A. U. }, title = {On spectral properties of $q$-oscillator operators }, journal = {Preprint ITP-92-59-E, Kiev }, volume = { }, number = { }, year = {1992 }, pages = { }, } @article{bukl2, author = {Burban, I. M. and Klimyk, A. U.}, title = {On spectral properties of $q$-oscillator operators}, journal = {Lett. Math. Phys.}, volume = {29}, year = {1993}, pages = {13--18}, } @ARTICLE{camp, author = {S. L. Campbell}, title = {Linear operators for which {$T^*T$} and {$TT^*$} commute ({II})}, journal = {Pacific Journ. 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Kyoto Univ.}, volume = {16}, year = {1980}, pages = {299--311}, } @book{ern, author = {Ernest, J. }, title = {Charting the operator terrain }, series = {Mem. Amer. Math. Soc. }, volume = {171 }, year = {1976 }, publisher = {Amer. Math. Soc.}, address = {Providence, R.I.}, } @ARTICLE{fa, author = {Ostrovski\u\i{}, V. L. and Samo\u\i{}lenko, Yu. S.}, title = {Families of unbounded selfadjoint operators, which are connected with non-{L}ie relations}, journal = {Funct. Anal. Prilozh.}, volume = {23}, number = {2}, year = {1989}, pages = {67--68}, note = {(Russian)} } @Article{flato, author = {Flato, M. and Simon, J. and Snellman, H. and Sternheimer, D.}, title = {Simple facts about analytic vectors and integrability}, journal = {Ann. Scient. de l'\'Ecole Norm. Sup.}, year = 1972, volume = 5, pages = {423--434} } @ARTICLE{ft, author = {Faddeev, L. D. and Takhtajan, L. A. }, title = {Liouville model on the lattice }, journal = {Lect. Notes Physics }, volume = {246 }, number = { }, year = {1986 }, pages = {166--179 }, } @ARTICLE{fu2, author = {Ostrovs'ky\u\i{}, V. L. and Samo\u\i{}lenko, Yu. S.}, title = {On representations of $*$-algebras in Mathematical Physics}, journal = {Nonlinear Mathematical Physics}, year = {1996}, volume = {3}, number = {1--2}, pages = {160--163} } @ARTICLE{gab, author = {Gabriel, P. }, title = {Unzerlegbare {D}arstellungen, {I} }, journal = {Manuscripta Math. }, volume = {6 }, number = { }, year = {1972 }, pages = {71 -- 103 }, } @ARTICLE{gavkl, author = {Gavrilik, A. M. and Klimyk, A. U. }, title = {$q$-deformed orthogonal and pseudoorthgonal algebras and their representations }, journal = {Lett. Math. Phys. }, volume = {21 }, number = { }, year = {1991 }, pages = {215 -- 220 }, } @ARTICLE{gelf_q, author = {Gelfand, I. M. and Fairlie, D. B. }, title = {The algebra of {W}eyl symmetrized polynomials and its quantum extension }, journal = {Commun. Math. Phys. }, volume = {136 }, number = {3 }, year = {1991 }, pages = {487--499 }, } @ARTICLE{gelpon, author = {Gel'fand, I. M. and Ponomarev, V. A. }, title = {Remarks on classification of a pair of commuting linear transformations in a finite-dimensional space }, journal = {Funct. Anal. i Prilozh. }, volume = {3 }, number = {4 }, year = {1969 }, pages = {81--82 }, note = {(Russian)}, } @Article{goldin, author = {Goldin, G. A. and Menikoff, R. and Sharp, D. H.}, title = {Particle statistics from induced representations of a local current group}, journal = {J. Math. Phys.}, year = 1980, volume = 21, number = 4, pages = {650--664} } @incollection{gorpod, author = {Gorodni\u\i{}, M. F. and Podkolzin, G. B.}, title = {Irreducible representations of a graded {L}ie algebra}, booktitle = {Spectral Theory of Operators and Infinite-dimensional Analysis}, publisher = {Inst. Math. Acad. Sci. Ukr. SSR, Kiev}, year = {1984}, pages = {66-76}, note = {(Russian)} } @article{greek, author = {Daskaloyanis, C.}, title = {Generalized deformed oscillator and nonlinear algebras}, journal = {J. Phys. A}, year = {1991}, volume = {24}, pages = {L789--L794}, } @ARTICLE{grzh, author = {Granovski\u\i{}, Ya. I. and Zhedanov, A. S. }, title = {Exactly solvable problems and their quadratic algebra }, journal = {Preprint Phys. Techn. Inst. Acad. Sci. Ukraine, Donetsk }, volume = { }, number = { }, year = {1989 }, pages = { }, note = {(Russian)}, } @ARTICLE{halm1, author = {Halmos, P. }, title = {Two subspaces }, journal = {Trans. Amer. Math. Soc. }, volume = {144 }, year = {1969 }, pages = {381--389 }, } @BOOK{halm2, author = {Halmos, P. }, title = {A {H}ilbert space problem book }, publisher = {Van Nostrand, Princeton }, year = {1967 }, note = { } } @ARTICLE{jimbo, author = {Jimbo, M. }, title = {A $q$-difference analogue of ${U}({\bf g})$ and the {Y}ang--{B}axter equation }, journal = {Lett. Math. Phys. }, volume = {10 }, number = {1 }, year = {1985 }, pages = {63--69 }, } @Book{jones89, author = {Jones, V. and Sunder, V. S.}, title = {Introduction to subfactors}, publisher = {Cambridge Univ. Press}, year = 1994, volume = 234, series = {London Math. Soc. Lect. Note. Ser.}, address = {Cambridge} } @Article{jor, author = {Bratteli, O. and J\o{}rgensen, P. E. T.}, title = {Isometries, shifts, {C}untz algebras and multiresolution wavelet analysis of scale {$N$}}, journal = {Int. Equat. Oper. Theory}, year = 1997, volume = 28, pages = {382--443} } @article{jorg, author = {J\o{}rgensen, P. E. T. and Schmitt, L. M. and Werner, R. F}, title = {Positive representation of general commutation relations allowing {W}ick ordering}, journal = {J. Funct. Anal.}, year = {1995}, volume = {134}, pages = {33--99}, } @Book{kad_rin, author = {Kadison, R. V. and Ringrose, J. R.}, title = {Fundamentals of the theory of operator algebras, {I}, {II}}, publisher = {Acad. 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Anal.}, volume = 115, number = 1, year = 1993, pages = {1--23}, } , note={(Russian)} } @article{koorn, author = {Koornwinder, T. H.}, title = {Positive convolution structures associated with quantum groups}, journal = {Probability measures on groups, X plenum}, year = {1991}, pages = {249--268}, } @INCOLLECTION{krug, author = {Kruglyak, S. A. }, title = {Representations of a quantum algegra related to the {Y}ang-{B}axter equation }, booktitle = {Spectral theory of operators and infinite-dimensional analysis }, publisher = {Inst. Math Acad. Sci. Ukraine, Kiev }, year = {1984 }, pages = {111 -- 120 }, note = {(Russian) } } @unpublished{krupir, author = {Kruglyak, S. and Piryatinskaya, A.}, title = {On unitary classification of weakly centered operators}, note = {to appear} } @ARTICLE{krusam, author = {Kruglyak, S. A. and Samo\u\i{}lenko, Yu. S. }, title = {On unitary equivalence of collections of self-adjoint operators }, journal = {Funct. Anal. i Prilozhen. }, volume = {14 }, number = {1 }, year = {1980 }, pages = {60--62 }, note = {(Russian)}, } @Article{kum, author = {Kumjan, A.}, title = {An involutive automorphism of the {B}unce--{D}eddens algebra}, journal = {Comptes Rendus Math. Rep de l'Acad. Sci. Canada}, year = 1988, volume = 10, pages = {217--218} } @Article{lac, author = {Laca, M.}, title = {Endomorphisms of {$\mathcal B(\mathcal H)$} and {C}untz algebras}, journal = {J. Oper. Theory}, year = 1993, volume = 30, pages = {85--101} } @ARTICLE{lomi, author = {Ostrovski\u\i{}, V. L. and Samo\u\i{}lenko, Yu. S. }, title = {Representations of $*$-algebras with two generators and polynomial relations }, journal = {Zap. Nauchn. Semin. LOMI }, volume = {172 }, number = {% }, year = {1989 }, pages = {121--129 }, note = {(Russian)} } @article{macf, author = {Macfarlane, A. J.}, title = {On $q$-analogues of the quantum harmonic oscillator and the quantum group $SU(2)$}, journal = {J. Phys. A}, volume = {22}, year = {1989}, pages = {4581--4586}, } @ARTICLE{mackey, author = {Mackey, G. W. }, title = {Induced representations of locally compact groups }, journal = {Ann. Math. }, volume = {55 }, number = {1 }, year = {1952 }, pages = {101--139 }, } @article{mackey1, author = {Mackey, G. W.}, title = {Imprimitivity for representations of locally compact groups}, journal = {Proc. Nat. Acad. Sci. USA}, volume = {35}, number = {9}, year = {1949}, pages = {537--545}, } @ARTICLE{mackey_imp, author = {Mackey, G. W. }, title = {Imprimitivity for representations of locally compact groups }, journal = {Proc. Nat. Acad. Sci. USA }, volume = {35 }, number = { }, year = {1949 }, pages = {537--545 }, } @ARTICLE{mis, author = {Misiurewicz, M. }, title = {Absolutely coninuous measures for certain maps of an interval }, journal = {Publ. Math. Inst. Hautes Etud. 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Phys.}, volume = {19}, number = {4}, year = {1990}, pages = {299--305}, } @article{ossilv, author = {Ostrovski\u\i{}, V. L. and Silvestrov, S. D.}, title = {Representations of the real forms of a graded analogue of the {L}ie algebra {$sl(2,\Bbb C)$}}, journal = {Ukr. Mat. Zhurn.}, year = {1992}, volume = {44}, number = {11}, pages = {1518--1524}, note = {(Russian)}, } @ARTICLE{ostur, author = {Ostrovsky\u\i{}, V. L. and Turovskaya, L. B.}, title = {Representations of $*$-algebras and multidimensional dynamical systems}, journal = {Ukr. Mat. Zhurn.}, volume = {47}, year = {1995}, number = {4}, pages = {488--497}, } @inproceedings{ostur2, author = {Ostrovs'ky\u\i{}, V.~L. and Turovskaya, L.~B.}, title = "On unbounded centered operators", booktitle = "International Workshop on Operator theory and Applications IWOTA~95. Final Programme and Book of Abstracts", year = "1995", publisher = "Univ. Regensburg", pages = "54--55", month = "July 31--August 4", } @book{partas, author = {Parthasarathy, K. R.}, title = {An introduction to quantum stochastic calculus}, publisher = {Birkh"auser--Verlag}, year = 1992, address = {Basel} } @ARTICLE{ped, author = {Pedersen, S. }, title = {Anticommuting selfadjoint operators }, journal = {J. Funct. Anal. }, volume = {89 }, number = {2 }, year = {1990 }, pages = {428--443 }, } @ARTICLE{ped2, author = {Pedersen, G. K.}, title = {Measure theory for {$C^*$}-algebras }, journal = {Math. Scand. }, volume = {22 }, year = {1968 }, pages = {63--74 }, } @ARTICLE{pirsam, author = {Piryatinskaya, A. Yu. and Samo\u\i{}lenko, Yu. S. }, title = {Wild problems in representation theory of $*$-algebras with generators and relations }, journal = {Ukr. Mat. Zhurn. }, volume = {47 }, number = {1 }, year = {1995 }, pages = {70--78}, note = {(Russian)} } @ARTICLE{podl, author = {Podle\'s P.}, title = {Quantum spheres}, journal = {Lett. Math. Phys.}, volume = {14}, year = {1987}, pages = {193--202}, } @Article{pop_snmp, author = {Popovych, S.}, title = {Representations of real forms of {W}itten's first deformation}, journal = {Symmetry Nonlin. Math. Phys.}, year = 1997, volume = 2, pages = {393--396} } @article{ppp, author = {Paulsen, V. and Pearcy, C. and Petrovi\v{c}, S.}, title = {On centered and weakly centered operators}, journal = {J. Funct. Anal.}, volume = {128}, year = {1995}, pages = {87--101}, } @ARTICLE{pusz, author = {Pusz, W. }, title = {On the implementation of {$S_\mu U(2)$} action in the irreducible representations of twisted canonical commutation relations }, journal = {Lett. Math. Phys. }, volume = {21 }, number = { }, year = {1991 }, pages = {59 -- 67 }, } @article{put, author = {Putnam, I.}, title = {The {$C^*$}-algebras associated with minimal homeomorphisms of the {C}antor set}, journal = {Pacific J. 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Phys.}, year = {1995}, volume = {35}, number = {2/3}, pages = {283--301}, } @BOOK{sch1, author = {Schm\"udgen, K. }, title = {Unbounded operator algebras and representation theory }, publisher = {Akademie-Verlag, Berlin }, year = {1990 }, note = { } } @ARTICLE{sch2, author = {Schm\"udgen, K. }, title = {Integrable operator representations of {$\Bbb R^2_q$} and {$SL_q(2,\Bbb R)$} }, journal = {Seminar Sophus Lie }, volume = {2 }, number = { }, year = {1992 }, pages = {107 -- 114 }, } @ARTICLE{sch3, author = {Schm\"udgen, K. }, title = {Integrable operator representations of {$\Bbb R^2_q$}, {$X_{q,\gamma}$} and {$SL_q(2, \Bbb R)$} }, journal = {Preprint, Leipzig }, volume = { }, number = { }, year = {1992 }, pages = { }, } @ARTICLE{sel, author = {Ostrovski\u\i{}, V. L.}, title = {Representations of a family of quadratic algebras with three generators}, journal = {Selecta Math. Sov.}, volume = 12, number = 2, year = 1993, pages = {119--127}, } @BOOK{shmr, author = {Sharkovski\u\i{}, A. N. and Maistrenko, Yu. L. and Romanenko, E. Yu. }, title = {Difference equations and their applications }, publisher = {Kluwer Acad. Publ. }, year = {1993 }, address = {Dordrecht }, note = {Transl. from Russian edn.: Naukova Dumka, Kiev, 1986}, } @ARTICLE{sklyan, author = {Sklyanin, E. K. }, title = {On some algebraic structures related to {Y}ang--{B}axter equation }, journal = {Funkt. Anal. i Prilozhen. }, volume = {16 }, number = {4 }, year = {1982 }, pages = {27--34 }, note = {(Russian)} } @ARTICLE{slie, author = {Ostrovsky\u\i{}, V.~L. and Samo\u\i{}lenko, Yu.~S.}, title = {On pairs of self-adjoint operators}, journal = {Seminar Sophus Lie}, volume = 3, number = 2, year = 1993, pages = {185--218}, } @BOOK{smst, author = {Smogorzhevski\u\i{}, A. S. and Stolova, E. 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