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Orthogonal Polynomials of Several Variables
 Encyclopedia of Mathematics and its Applications
, 2001
"... Abstract. We report on the recent development on the general theory of orthogonal polynomials in several variables, in which results parallel to the theory of orthogonal polynomials in one variable are established using a vectormatrix notation. 1 ..."
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Cited by 236 (44 self)
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Abstract. We report on the recent development on the general theory of orthogonal polynomials in several variables, in which results parallel to the theory of orthogonal polynomials in one variable are established using a vectormatrix notation. 1
IN SEVERAL VARIABLES
, 2003
"... Abstract. For a convex, real function f we present a simple proof of the formula Tr(f ( ∑m k=1 a ∗ kxkak)) ≤ Tr ( ∑m k=1 a ∗ kf(xk)ak), valid for each tuple (x1,..., xm) of symmetric matrices in Mn and every unital column (a1,..., am) of matrices, i.e. ∑m k=1 a ∗ kak = 1. This is the standard Jense ..."
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Cited by 11 (0 self)
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Jensen trace inequality. If f ≥ 0 it holds also for the unbounded trace on B(H), where H is an infinitedimensional Hilbert space. We then investigate the more general case where τ is a densely defined, lower semicontinuous trace on a C∗−algebra A and f is a convex, continuous function of n variables
STOLARSKY MEANS OF SEVERAL VARIABLES
, 2005
"... Communicated by Zs. Páles ABSTRACT. A generalization of the Stolarsky means to the case of several variables is presented. The new means are derived from the logarithmic mean of several variables studied in [9]. Basic properties and inequalities involving means under discussion are included. Limit t ..."
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Cited by 1 (0 self)
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Communicated by Zs. Páles ABSTRACT. A generalization of the Stolarsky means to the case of several variables is presented. The new means are derived from the logarithmic mean of several variables studied in [9]. Basic properties and inequalities involving means under discussion are included. Limit
Polynomial interpolation in several variables
, 2000
"... This is a survey of the main results on multivariate polynomial interpolation in the last twentyfive years, a period of time when the subject experienced its most rapid development. The problem is considered from two different points of view: the construction of data points which allow unique inter ..."
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Cited by 71 (7 self)
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This is a survey of the main results on multivariate polynomial interpolation in the last twentyfive years, a period of time when the subject experienced its most rapid development. The problem is considered from two different points of view: the construction of data points which allow unique interpolation for given interpolation spaces as well as the converse. In addition, one section is devoted to error formulas and another to connections with computer algebra. An extensive list of references is also included.
Notes on series in several variables
"... These notes are elementary derivations of wellknown, but sometimes hard to find, facts on series in several variables. By "elementary " I mean "avoiding the theory of complex differentiation and integration, " and the basic ideas of the proofs will be natural gen ..."
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These notes are elementary derivations of wellknown, but sometimes hard to find, facts on series in several variables. By "elementary " I mean "avoiding the theory of complex differentiation and integration, " and the basic ideas of the proofs will be natural
Polynomials of Several Variables
, 2002
"... We consider the set σP of the power nonnegative polynomials of several variables.By QP we denote the class of the polynomials from σ1 which can be represented as a sum of squares.It is shown in the classic work by D.Hilbert[3] that QP does not coincide with σP.Step by step a number of polynomials ..."
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We consider the set σP of the power nonnegative polynomials of several variables.By QP we denote the class of the polynomials from σ1 which can be represented as a sum of squares.It is shown in the classic work by D.Hilbert[3] that QP does not coincide with σP.Step by step a number of polynomials
QUASISUMS IN SEVERAL VARIABLES
"... Abstract. In this note we introduce the notions of quasisums and of the local quasisums in several variables, respectively. We prove that the local quasisums are also quasisums. We show how this result can be applied to find the continuous solutions of the functional equation g(u11 + · · ·+ u1N ..."
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Abstract. In this note we introduce the notions of quasisums and of the local quasisums in several variables, respectively. We prove that the local quasisums are also quasisums. We show how this result can be applied to find the continuous solutions of the functional equation g(u11 + · · ·+ u1
Maximum Likelihood Phylogenetic Estimation from DNA Sequences with Variable Rates over Sites: Approximate Methods
 J. Mol. Evol
, 1994
"... Two approximate methods are proposed for maximum likelihood phylogenetic estimation, which allow variable rates of substitution across nucleotide sites. Three data sets with quite different characteristics were analyzed to examine empirically the performance of these methods. The first, called ..."
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Cited by 557 (29 self)
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Two approximate methods are proposed for maximum likelihood phylogenetic estimation, which allow variable rates of substitution across nucleotide sites. Three data sets with quite different characteristics were analyzed to examine empirically the performance of these methods. The first, called
Polynomial Interpolation in Several Variables
, 1994
"... INTRODUCTION One of the things I changed rather drastically in that textbook was the treatment of polynomial interpolation. I was then (and still am) much impressed with the e#ciency of the divided di#erence notion. It is a somewhat tricky Notion for the beginning student, and its treatment in the ..."
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Cited by 16 (2 self)
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INTRODUCTION One of the things I changed rather drastically in that textbook was the treatment of polynomial interpolation. I was then (and still am) much impressed with the e#ciency of the divided di#erence notion. It is a somewhat tricky Notion for the beginning student, and its treatment in the current edition is still not quite right. Perhaps we will get it right in the next one. In any case, polynomial interpolation occurs in the first real chapter of the book since polynomial interpolation is fundamental to much of numerical analysis. It has therefore been something of a puzzle and disappointment to me that there is not a theory of multivariate polynomial interpolation as elegant and convincing and as basic as the univariate theory. The trouble is easy to spot: Univariate polynomial interpolation starts with the observation that, for every set # of k + 1 points, and for every function f defined (at 2 least) on #,
Operator monotone functions of several variables
 Math. Ineq. Appl
"... We propose a notion of operator monotonicity for functions of several variables, which extends the well known notion of operator monotonicity for functions of only one variable. The notion is chosen such that a fundamental relationship between operator convexity and operator monotonicity for functio ..."
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Cited by 9 (2 self)
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We propose a notion of operator monotonicity for functions of several variables, which extends the well known notion of operator monotonicity for functions of only one variable. The notion is chosen such that a fundamental relationship between operator convexity and operator monotonicity
Results 1  10
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35,242