메뉴 건너뛰기




Volumn 54, Issue 1, 2005, Pages 189-226

Truncated K-moment problems in several variables

Author keywords

Flat extensions of positive matrices; Localizing matrix; Moment matrix extension; Semi algebraic sets; Several variables; Truncated moment problem

Indexed keywords


EID: 27844587887     PISSN: 03794024     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (182)

References (54)
  • 2
    • 84972553791 scopus 로고
    • A moment problem for positive measures on the unit disc
    • A. ATZMON, A moment problem for positive measures on the unit disc, Pacific J. Math. 59(1975), 317-325.
    • (1975) Pacific J. Math. , vol.59 , pp. 317-325
    • Atzmon, A.1
  • 3
    • 0000203558 scopus 로고
    • A remark on the multidimensional moment problem
    • C. BERG, J. CHRISTENSEN, C. JENSEN, A remark on the multidimensional moment problem, Math. Ann. 243(1979), 163-169.
    • (1979) Math. Ann. , vol.243 , pp. 163-169
    • Berg, C.1    Christensen, J.2    Jensen, C.3
  • 4
    • 0000396067 scopus 로고
    • Polynomially positive definite sequences
    • C. BERG, P. MASERICK, Polynomially positive definite sequences, Math. Ann. 259 (1982), 487-495.
    • (1982) Math. Ann. , vol.259 , pp. 487-495
    • Berg, C.1    Maserick, P.2
  • 5
    • 0000893882 scopus 로고
    • n et décompositions de polynômes a plusieurs variables
    • n et décompositions de polynômes a plusieurs variables, J. Funct. Anal. 58(1984), 254-266.
    • (1984) J. Funct. Anal. , vol.58 , pp. 254-266
    • Cassier, G.1
  • 6
    • 0029684826 scopus 로고    scopus 로고
    • Solution of the truncated complex moment problem for flat data
    • R.E. CURTO, L. A. FIALKOW, Solution of the truncated complex moment problem for flat data, Mem. Amer. Math. Soc. 119(1996), no. 568.
    • (1996) Mem. Amer. Math. Soc. , vol.119 , Issue.568
    • Curto, R.E.1    Fialkow, L.A.2
  • 7
    • 0001881572 scopus 로고    scopus 로고
    • Flat extensions of positive moment matrices: Relations in analytic or conjugate terms
    • Birkhäuser Verlag, Basel
    • R. CURTO, L. FIALKOW, Flat extensions of positive moment matrices: Relations in analytic or conjugate terms, Oper. Theory Adv. Appl., vol. 104, Birkhäuser Verlag, Basel 1998, pp. 59-82.
    • (1998) Oper. Theory Adv. Appl. , vol.104 , pp. 59-82
    • Curto, R.1    Fialkow, L.2
  • 8
    • 21944445317 scopus 로고    scopus 로고
    • Flat extensions of positive moment matrices: Recursively generated relations
    • R. CURTO, L. FIALKOW, Flat extensions of positive moment matrices: Recursively generated relations, Mem. Amer. Math. Soc. 136(1998), no. 648.
    • (1998) Mem. Amer. Math. Soc. , vol.136 , Issue.648
    • Curto, R.1    Fialkow, L.2
  • 9
    • 0000728349 scopus 로고    scopus 로고
    • The quadratic moment problem for the unit disk and unit circle
    • R. CURTO, L. FIALKOW, The quadratic moment problem for the unit disk and unit circle, Integral Equations Operator Theory 38(2000), 377-409.
    • (2000) Integral Equations Operator Theory , vol.38 , pp. 377-409
    • Curto, R.1    Fialkow, L.2
  • 10
    • 23044517911 scopus 로고    scopus 로고
    • The truncated complex K-moment problem
    • R. CURTO, L. FIALKOW, The truncated complex K-moment problem, Trans. Amer. Math. Soc. 352(2000), 2825-2855.
    • (2000) Trans. Amer. Math. Soc. , vol.352 , pp. 2825-2855
    • Curto, R.1    Fialkow, L.2
  • 11
    • 0037095604 scopus 로고    scopus 로고
    • A duality proof of Tchakaloff's theorem
    • R. CURTO, L. FIALKOW, A duality proof of Tchakaloff's theorem, J. Math. Anal. Appl. 269(2002), 519-532.
    • (2002) J. Math. Anal. Appl. , vol.269 , pp. 519-532
    • Curto, R.1    Fialkow, L.2
  • 12
    • 0036763607 scopus 로고    scopus 로고
    • Solution of the singular quartic moment problem
    • R. CURTO, L. FIALKOW, Solution of the singular quartic moment problem, J. Operator Theory 48(2002), 315-354.
    • (2002) J. Operator Theory , vol.48 , pp. 315-354
    • Curto, R.1    Fialkow, L.2
  • 13
    • 11144290607 scopus 로고    scopus 로고
    • Solution of the truncated parabolic moment problem
    • R. CURTO, L. FIALKOW, Solution of the truncated parabolic moment problem, Integral Equations Operator Theory 50(2004), 169-196.
    • (2004) Integral Equations Operator Theory , vol.50 , pp. 169-196
    • Curto, R.1    Fialkow, L.2
  • 14
    • 21644478264 scopus 로고    scopus 로고
    • Solution of the truncated hyperbolic moment problem
    • R. CURTO, L. FIALKOW, Solution of the truncated hyperbolic moment problem, Integral Equations Operator Theory 52(2005), 181-218.
    • (2005) Integral Equations Operator Theory , vol.52 , pp. 181-218
    • Curto, R.1    Fialkow, L.2
  • 15
    • 0034660836 scopus 로고    scopus 로고
    • Moments and positivity
    • O. DEMANZE, Moments and positivity, J. Math. Anal. Appl. 247(2000), 570-587.
    • (2000) J. Math. Anal. Appl. , vol.247 , pp. 570-587
    • Demanze, O.1
  • 16
    • 24144451751 scopus 로고    scopus 로고
    • Can a minimal degree 6 cubature rule for the disk have all points inside?
    • C. EASWARAN, L. FIALKOW, S. PETROVIC, Can a minimal degree 6 cubature rule for the disk have all points inside?, J. Comput. Appl. Math., to appear.
    • J. Comput. Appl. Math.
    • Easwaran, C.1    Fialkow, L.2    Petrovic, S.3
  • 17
    • 0000362253 scopus 로고
    • Positivity, extensions and the truncated complex moment problem
    • L. FIALKOW, Positivity, extensions and the truncated complex moment problem, Contemp. Math. 185(1995), 133-150.
    • (1995) Contemp. Math. , vol.185 , pp. 133-150
    • Fialkow, L.1
  • 18
    • 0001297038 scopus 로고    scopus 로고
    • Minimal representing measures arising from rank-increasing moment matrix extensions
    • L. FIALKOW, Minimal representing measures arising from rank-increasing moment matrix extensions, J. Operator Theory 42(1999), 425-436.
    • (1999) J. Operator Theory , vol.42 , pp. 425-436
    • Fialkow, L.1
  • 19
    • 0037275929 scopus 로고    scopus 로고
    • Truncated complex moment problems with a ZZ̄ relation
    • L. FIALKOW, Truncated complex moment problems with a ZZ̄ relation, Integral Equations Operator Theory 45(2003), 405-435.
    • (2003) Integral Equations Operator Theory , vol.45 , pp. 405-435
    • Fialkow, L.1
  • 21
    • 0001923625 scopus 로고
    • The multidimensional moment problem
    • B. FUGLEDE, The multidimensional moment problem, Exposition. Math. 1(1983), 47-65.
    • (1983) Exposition. Math. , vol.1 , pp. 47-65
    • Fuglede, B.1
  • 22
    • 0001656889 scopus 로고
    • On the momentum problem for distributions in more than one dimension. I
    • E.K. HAVILAND, On the momentum problem for distributions in more than one dimension. I, Amer. J. Math. 57(1935), 562-568;
    • (1935) Amer. J. Math. , vol.57 , pp. 562-568
    • Haviland, E.K.1
  • 23
    • 0000336262 scopus 로고
    • On the momentum problem for distributions in more than one dimension. II
    • On the momentum problem for distributions in more than one dimension. II, Amer. J. Math. 58(1936), 164-168.
    • (1936) Amer. J. Math. , vol.58 , pp. 164-168
  • 25
    • 0036830643 scopus 로고    scopus 로고
    • Positivity, sums of squares and the multidimensional moment problem
    • S. KUHLMANN, M. MARSHALL, Positivity, sums of squares and the multidimensional moment problem, Trans. Amer. Math. Soc. 354(2002), 4285-4301.
    • (2002) Trans. Amer. Math. Soc. , vol.354 , pp. 4285-4301
    • Kuhlmann, S.1    Marshall, M.2
  • 26
    • 0035238864 scopus 로고    scopus 로고
    • Global optimization with polynomials and the problem of moments
    • J.B. LASSERRE, Global optimization with polynomials and the problem of moments, SIAM J. Optim. 11(2001), 796-817.
    • (2001) SIAM J. Optim. , vol.11 , pp. 796-817
    • Lasserre, J.B.1
  • 27
    • 0036387295 scopus 로고    scopus 로고
    • Bounds on measures satisfying moment conditions
    • J.B. LASSERRE, Bounds on measures satisfying moment conditions, Ann. Appl. Probab. 12(2002), 1114-1137.
    • (2002) Ann. Appl. Probab. , vol.12 , pp. 1114-1137
    • Lasserre, J.B.1
  • 28
    • 0036034519 scopus 로고    scopus 로고
    • Polynomials nonnegative on a grid and discrete optimization
    • J.B. LASSERRE, Polynomials nonnegative on a grid and discrete optimization, Trans. Amer. Math. Soc. 354(2002), 631-649.
    • (2002) Trans. Amer. Math. Soc. , vol.354 , pp. 631-649
    • Lasserre, J.B.1
  • 29
    • 18744395436 scopus 로고    scopus 로고
    • Semidefinite representations for finite varieties
    • M. LAURENT, Semidefinite representations for finite varieties, Math. Programming, to appear.
    • Math. Programming
    • Laurent, M.1
  • 30
    • 0141517272 scopus 로고    scopus 로고
    • A comparison of the Sherali-Adams, Lovász-Schrijver and Lasserre relaxations for 0-1 programming
    • M. LAURENT, A comparison of the Sherali-Adams, Lovász-Schrijver and Lasserre relaxations for 0-1 programming, Math. Oper. Res. 28(2003), 470-496.
    • (2003) Math. Oper. Res. , vol.28 , pp. 470-496
    • Laurent, M.1
  • 31
    • 26444549416 scopus 로고    scopus 로고
    • Revisiting two theorems of Curto and Fialkow on moment matrices
    • M. LAURENT, Revisiting two theorems of Curto and Fialkow on moment matrices, Proc. Amer. Math. Soc. 133(2005), 2965-2976.
    • (2005) Proc. Amer. Math. Soc. , vol.133 , pp. 2965-2976
    • Laurent, M.1
  • 32
    • 23044523312 scopus 로고    scopus 로고
    • Polynomials that are positive on an interval
    • V. POWERS, B. REZNICK, Polynomials that are positive on an interval, Trans. Amer. Math. Soc. 352(2000), 4677-4692.
    • (2000) Trans. Amer. Math. Soc. , vol.352 , pp. 4677-4692
    • Powers, V.1    Reznick, B.2
  • 33
    • 0001276275 scopus 로고    scopus 로고
    • A new bound for Pólya's theorem with applications to polynomials positive on polyhedra
    • V. POWERS, B. REZNICK, A new bound for Pólya's theorem with applications to polynomials positive on polyhedra, J. Pure Appl. Algebra 164(2001), 221-229.
    • (2001) J. Pure Appl. Algebra , vol.164 , pp. 221-229
    • Powers, V.1    Reznick, B.2
  • 34
    • 0005232063 scopus 로고    scopus 로고
    • The moment problem for non-compact semialgebraic sets
    • V. POWERS, C. SCHEIDERER, The moment problem for non-compact semialgebraic sets, Adv. Geom. 1(2001), 71-88.
    • (2001) Adv. Geom. , vol.1 , pp. 71-88
    • Powers, V.1    Scheiderer, C.2
  • 35
    • 27844478040 scopus 로고    scopus 로고
    • Bounds for representations of polynomials positive on compact semi-algebraic sets
    • Fields Inst. Commun., Amer. Math. Soc., Providence, RI
    • A. PRESTEL, Bounds for representations of polynomials positive on compact semi-algebraic sets, in Valuation Theory and its Applications, vol. I (Saskatoon, SK, 1999), Fields Inst. Commun., vol. 32, Amer. Math. Soc., Providence, RI 2002, pp. 253-260.
    • (2002) Valuation Theory and Its Applications, Vol. I (Saskatoon, SK, 1999) , vol.1-32 , pp. 253-260
    • Prestel, A.1
  • 36
    • 38249026822 scopus 로고
    • A two-dimensional moment problem
    • M. PUTINAR, A two-dimensional moment problem, J. Funct. Anal. 80(1988), 1-8.
    • (1988) J. Funct. Anal. , vol.80 , pp. 1-8
    • Putinar, M.1
  • 37
    • 0000135301 scopus 로고
    • Positive polynomials on compact semi-algebraic sets
    • M. PUTINAR, Positive polynomials on compact semi-algebraic sets, Indiana Univ. Math. J. 42(1993), 969-984.
    • (1993) Indiana Univ. Math. J. , vol.42 , pp. 969-984
    • Putinar, M.1
  • 38
    • 21744461770 scopus 로고    scopus 로고
    • On Tchakaloff's Theorem
    • M. PUTINAR, On Tchakaloff's Theorem, Proc. Amer. Math. Soc. 125(1997), 2409-2414.
    • (1997) Proc. Amer. Math. Soc. , vol.125 , pp. 2409-2414
    • Putinar, M.1
  • 39
    • 0033416838 scopus 로고    scopus 로고
    • Solving moment problems by dimensional extension
    • M. PUTINAR, F.-H. VASILESCU, Solving moment problems by dimensional extension, Ann. of Math. 149(1999), 1087-1107.
    • (1999) Ann. of Math. , vol.149 , pp. 1087-1107
    • Putinar, M.1    Vasilescu, F.-H.2
  • 40
    • 0001667254 scopus 로고
    • Sums of even powers of real linear forms
    • B. REZNICK, Sums of even powers of real linear forms, Mem. Amer. Math. Soc. 96(1992), no. 463.
    • (1992) Mem. Amer. Math. Soc. , vol.96 , Issue.463
    • Reznick, B.1
  • 42
    • 33646876901 scopus 로고    scopus 로고
    • Sums of squares of regular functions on real algebraic varieties
    • C. SCHEIDERER, Sums of squares of regular functions on real algebraic varieties, Trans. Amer. Math. Soc. 352(2000), 1039-1069.
    • (2000) Trans. Amer. Math. Soc. , vol.352 , pp. 1039-1069
    • Scheiderer, C.1
  • 43
    • 0001250675 scopus 로고
    • The K-moment problem for compact semi-algebraic sets
    • K. SCHMÜDGEN, The K-moment problem for compact semi-algebraic sets, Math. Ann. 289(1991), 203-206.
    • (1991) Math. Ann. , vol.289 , pp. 203-206
    • Schmüdgen, K.1
  • 45
    • 0000030826 scopus 로고
    • An operator Hellinger integral
    • J.L. SMUL'JAN, An operator Hellinger integral, [Russian], Mat. Sb. (N.S.) 49(1959), 381-430.
    • (1959) Mat. Sb. (N.S.) , vol.49 , pp. 381-430
    • Smul'jan, J.L.1
  • 46
    • 0001399197 scopus 로고
    • Moment functions on real algebraic sets
    • J. STOCHEL, Moment functions on real algebraic sets, Ark. Mat. 30(1992), 133-148.
    • (1992) Ark. Mat. , vol.30 , pp. 133-148
    • Stochel, J.1
  • 47
    • 0035568273 scopus 로고    scopus 로고
    • Solving the truncated moment problem solves the moment problem
    • J. STOCHEL, Solving the truncated moment problem solves the moment problem, Glasgow J. Math. 43(2001), 335-341.
    • (2001) Glasgow J. Math. , vol.43 , pp. 335-341
    • Stochel, J.1
  • 48
    • 0001998633 scopus 로고
    • Algebraic operators and moments on algebraic sets
    • J. STOCHEL, F.H. SZAFRANIEC, Algebraic operators and moments on algebraic sets, Portugal. Math. 51(1994), 25-15.
    • (1994) Portugal. Math. , vol.51 , pp. 25-115
    • Stochel, J.1    Szafraniec, F.H.2
  • 49
    • 0000055633 scopus 로고    scopus 로고
    • The complex moment problem and subnormality: A polar decomposition approach
    • J. STOCHEL, F.H. SZAFRANIEC, The complex moment problem and subnormality: A polar decomposition approach, J. Funct. Anal. 159(1998), 432-491.
    • (1998) J. Funct. Anal. , vol.159 , pp. 432-491
    • Stochel, J.1    Szafraniec, F.H.2
  • 51
    • 0000300752 scopus 로고
    • Boundedness of the shift operator related to positive definite forms: An application to moment problems
    • F.H. SZAFRANIEC, Boundedness of the shift operator related to positive definite forms: an application to moment problems, Ark. Mat. 19(1981), 251-259.
    • (1981) Ark. Mat. , vol.19 , pp. 251-259
    • Szafraniec, F.H.1
  • 53
    • 0001630435 scopus 로고
    • Formules de cubatures mécaniques à coefficients non négatifs
    • V. TCHAKALOFF, Formules de cubatures mécaniques à coefficients non négatifs, Bull. Sci. Math. 81(1957), 123-134.
    • (1957) Bull. Sci. Math. , vol.81 , pp. 123-134
    • Tchakaloff, V.1
  • 54
    • 0003503814 scopus 로고    scopus 로고
    • Wolfram Research, Inc., Champaign, IL
    • WOLFRAM RESEARCH, INC., Mathematica, Version 3.0, Wolfram Research, Inc., Champaign, IL 1996.
    • (1996) Mathematica, Version 3.0


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.