"Minoru Murata,Tetsuo Tsuchida","Parabolic Martin boundaries and asymptotic formulas of heat kernels for one-dimensional elliptic operators with periodic coefficients",,"Potential Analysis","Springer","Volume 33","Number 4","pp. 387--414",2010,Oct. "Pedro J. Mendez-Hernandez, Minoru Murata","Semismall perturbations, semi-intrinsic ultracontractivity, and integral representations of nonnegative solutions for parabolic equations",,"Journal of Functional Analysis","Elsevier Inc.","Vol. 257",,"pp. 1799?1827",2009,July "Minoru Murata","Integral represntations of nonnegative solutions for parabolic equations and elliptic Martin boundaries",,"J. Func. Anal.","Elsevier","Vol. 245",,"pp. 177-212",2007, "‘บ“c›‰ฅ‘q“c˜a_","‘ศ‰~Œ^E•๚•จŒ^•ฮ”๗•ช•๛’๖Žฎ",,,"Šโ”g‘“X",,,,2006,May "Minoru Murata","Representations of nonnegative solutions for parabolic equations",,"Advanced Studies in Pure Mathematics",,"Vol. 44",,"pp. 283-289",2006, "Minoru Murata,Tetsuo Tsuchida","Asymptotics of Green functions and the limiting absorption principle for elliptic operators with periodic coefficients",,"J. Math. Kyoto Univ.","Kyoto Univ.","Vol. 46",,"pp. 713-754",2006, "Minoru Murata","Uniqueness theorems for parabolic equations and Martin boundaries for elliptic equations in skew product form",,"J. Math. Soc. Japan",,"Vol. 57","No. 2","pp. 387-413",2005,Apr. "M. Murata,T. Tsuchida","Asymptotics of Green functions and Martin boundaries for elliptic operators with periodic coefficients",,"J. Diff. Eq.",,"Vol. 195",,"pp. 82-118",2003, "Minoru Murata","Heat escape",,"Math. Ann.",,"Vol. 327",,"pp. 203-226",2003, "Minoru Murata","Martin boundaries of elliptic skew products, semismall perturbations, and fundamental solutions of parabolic equations",,"J. Functional Analysis",,"Vol. 194","No. 1","pp. 53-141",2002, "K. Ishige,M. Murata","Uniqueness of nonnegative solutions of the Cauchy problem for parabolic equations on manifolds or domains",,"Ann. Scuola Norm. Sup. Pisa",,"Vol. 30","No. 1","pp. 171-223",2001, "Minoru Murata","Structure of positive solutions to Schroedinger equations",,"Sugaku Expositions",,"Vol. 11",,"pp. 101-121",1998, "K. Ishige,M. Murata","An intrinsic metric approach to uniqueness of the positive Cauchy problem for parabolic equations",,"Math. Z",,"Vol. 227",,"pp. 313-335",1998, "Minoru Murata","Semismall perturbations in the Martin theory for elliptic equations",,"Israel J. Math",,"Vol. 102",,"pp. 29-60",1997, "‘บ“c›‰@‘q“c˜aO","•ฮ”๗•ช•๛’๖Žฎ1(Šโ”guภ Œป‘ใ”Šw‚ฬŠ๎‘b)",,"Šโ”g‘“X","Šโ”g‘“X",,,,1997, "Minoru Murata","Non-uniqueness of the positive Dirichlet problem for parabolic equations in cylinders",,"J. Funct. Anal.",,"Vol. 135","No. 2","pp. 456-487",1996, "H. Aikawa,M. Murata","Generalized Cranston-McConnell inequalities and Martin boundaries of unbounded domains",,"J. Anal. Math.",,"Vol. 69",,"pp. 137-152",1996, "Minoru Murata","Uniqueness and non-uniqueness of the positive Cauchy problem for the heat equation on Riemannian manifolds",,"Proc. Amer. Math. Soc",,"Vol. 123",,"pp. 1923-1932",1995, "Minoru Murata","Non-uniqueness of the positive Cauchy problem for parabolic equations",,"J. Differential Eq.",,"Vol. 123","No. 2","pp. 343-387",1995, "‘บ“c›‰","Schroedinger•๛’๖Žฎ‚ฬณ’l‰๐‚ฬ\‘ข",,"”Šw(“๚–{”Šw‰๏•าW)",,"Vol. 47",,"pp. 360-376",1995, "Minoru Murata","Sufficient condition for non-uniqueness of the positive Cauchy problem for parabolic equations",,"Spectral and Scattering Theory, Advanced Studies in Pure Math",,"Vol. 23","No. 1","pp. 275-282",1994, "Minoru Murata","Uniform restricted parabolic Harnack inequality, separation principle, and ultracontractivity for parabolic equations",,"Functional Analysis and Related Topics, 1991, Lecture Notes in Math",,"Vol. 1540","No. 1","pp. 277-288",1993, "Minoru Murata","Positive harmonic functions on rotationarysymmetric Riemannian manifolds",,"Potential Theory, Walte de Gruyter & Co.",,,,"pp. 251-259",1992, "Minoru Murata","On construction of Martin boundaries for second order elliptic equations",,"Publ. RIMS, Kyoto Univ",,"Vol. 26",,"pp. 585-627",1990, "Minoru Murata","Martin compactification and asymptotics of Green functions for Schroedinger operators with anisotropic potentials",,"Math. Ann.",,"Vol. 288",,"pp. 211-230",1990, "Minoru Murata","Structure of positive solutions to(-ข+V)u=0 in Rn",,"Differential Equations and Mathematical Physics, Lecture Notes in Math.",,"Vol. 1285","No. 1","pp. 342-347",1988, "Minoru Murata","Isolated singularities and positive solutions of elliptic equations in Rn",,"Proc. Japan Acad.",,"Vol. 63","No. Ser.A","pp. 146-148",1987, "Minoru Murata","Structure of positive solutions to(-ข+V)u=0 in Rn",,"Duke Math. J.",,"Vol. 53","No. 4","pp. 869-943",1986, "Minoru Murata","Finiteness of negative spectra of elliptic operators",,"Canad. Math. Bull.",,"Vol. 28",,"pp. 487-491",1985, "Minoru Murata","Large time asymptotics for fundamental solutions of diffusion equations",,"Tohoku Math. J",,"Vol. 37","No. 2","pp. 151-195",1985, "Minoru Murata","Isomorphism theorems for elliptic operators in R^n",,"Comm. in Partial Differential Equations",,"Vol. 9",,"pp. 1085-1105",1984, "Minoru Murata","Positive solutions and large time behaviors of Schroedinger semigroups, Simon's problem",,"J. Functional Analysis",,"Vol. 56",,"pp. 300-310",1984, "Minoru Murata","High energy resolvent estimates, II, higher order elliptic operators",,"J. Math. Soc. Japan",,"Vol. 36",,"pp. 1-10",1984, "Minoru Murata","High energy resolvent estimates, I, first order operators",,"J. Math. Soc. Japan",,"Vol. 35",,"pp. 711-733",1983, "Minoru Murata","Asymptotic expansions in time for solutions of Schroedinger type equations",,"J. Functional Analysis",,"Vol. 49","No. 1","pp. 10-56",1982, "Minoru Murata","Characterizations of the ranges of wave operators for symmetric systems and an application",,"Tokyo J. Math",,"Vol. 4",,"pp. 113-132",1981, "‘บ“c›‰","•ฮ”๗•ช•๛’๖Žฎ‚ฬ‰๐‚ฬ–ณŒภ‰“‚ษ‚จ‚ฏ‚้‘‘ๅ“x‚ฬ‰บŒภ",,"”Šw(“๚–{”Šw‰๏•าW)",,"Vol. 32",,"pp. 1-16",1980, "Minoru Murata","Rate of decay of local energy and spectral properties of elliptic operators",,"Japanese J. Math",,"Vol. 6",,"pp. 77-127",1980, "Minoru Murata","Rate of decay of local energy and wave operators for symmetric systems",,"J. Math. Soc. Japan",,"Vol. 31",,"pp. 451-480",1979, "‘บ“c›‰","‘ศ‰~Œ^์—p‘f‚ฬƒXƒyƒNƒgƒ‹‚ฬซŽฟ‚ฦ‹วŠƒGƒlƒ‹ƒM[‚ฬŒธŠ“x",,,,,,,1979, "Minoru Murata","Finiteness of eigenvalues of self-adjoint elliptic operators",,"J. Fac. Sci. Univ. Tokyo, Sec IA",,"Vol. 25",,"pp. 205-218",1978, "Minoru Murata","Lower bounds at infinity of solutions of partial differential equations in the exterior of a proper cone",,"Israel J. Math",,"Vol. 31",,"pp. 193-203",1978, "Minoru Murata","Scattering solutions decay at least logarithmically",,"Proc. Japan Acad",,"Vol. 54","No. Ser.A","pp. 42-45",1978, "Minoru Murata","Asymptotic behaviors at infinity of solutions of certain linear partial differential equations",,"J. Fac. Sci. Univ. Tokyo, Sec. IA",,"Vol. 23",,"pp. 107-148",1976, "Minoru Murata","A theorem of Liouville type for partial differential equations with constant coefficients",,"J. Fac. Sci. Univ. Tokyo, Sec. IA",,"Vol. 21",,"pp. 395-404",1974, "Minoru Murata","Anti-locality of certain functions of the Laplace operator",,"J. Math. Soc. Japan",,"Vol. 25",,"pp. 556-564",1973,