Extending means to several variables
نویسندگان
چکیده
منابع مشابه
Extending Means of Two Variables to Several Variables
We present a method, based on series expansions and symmetric polynomials, by which a mean of two variables can be extended to several variables. We apply it mainly to the logarithmic mean.
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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 theorems for these means with the underlying measure being the Dirichlet measure are established.
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Cesàro (C, δ) means are studied for orthogonal expansions with respect to the weight function ∏d i=1 |xi |2κi on the unit sphere, and for the corresponding weight functions on the unit ball and the Jacobi weight on the simplex. A sharp pointwise estimate is established for the (C, δ) kernel with δ >−1 and for the kernel of the projection operator, which allows us to derive the exact order for t...
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This text is a short two hour introduction into the theory of several complex variables. These lectures were given in May 1996 at Caltech to the class Ma 108 substituting for someone else. As prerequisite, the topic requires some familiarity with complex analysis in one dimension. The higher dimensional generalization of complex analysis in one variables is an important part of mathematics. Our...
متن کاملIntroduction to Calculus in Several Variables
1 2 Contents 0. One-variable calculus 1. The derivative 2. Inverse function and implicit function theorem 3. Fundamental local existence theorem for ODE 4. The Riemann integral in n variables 5. Integration on surfaces 6. Differential forms 7. Products and exterior derivatives of forms 8. The general Stokes formula 9. The classical Gauss, Green, and Stokes formulas 10. Holomorphic functions and...
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2020
ISSN: 1331-4343
DOI: 10.7153/mia-2020-23-01