For our purposes we choose the language of majorizing measures. Majorizing measures in the orthogonal setting Majorizing measures were invented to characterize sample boundedness for certain stochastic processes. By Theorem 3.
Then appeared the characterization of sample boundedness for Gaussian processes  and many other canonical processes [11,5]. Also, the author could generalize the result for the ultrametric spaces to a setting  which in the special suborthogonal case gives: W. I — Theorem 5. Consequently Theorems 4 and 5 imply that the sample boundedness of all suborthogonal processes on T is equivalent to the existence of a majorizing measure. Theorem 6. Now we turn to the main question of characterizing 1.
Our main result is the following: Theorem 7. I — Proposition 8.
Convergence Problems Orthogonal Series by Alexits Prof
References  W. Bednorz, A theorem on majorizing measures, Ann. Bednorz, Majorizing measures on metric spaces, C. I 1—2 75— Kashin, A. Latala, Sudakov minoration principle and supremum of some processes, Geom.
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Preface Chapter I Fundamental Ideas. Examples of Series of Orthogonal Functions 1. Orthogonality, Orthogonalization, Series of Orthogonal Functions 2.
- Convergence Problems Orthogonal Series by Alexits Prof - AbeBooks.
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The Riesz-Fischer Theorem. Complete Orthogonal Systems 3. Orthogonal Polynomials 4. The Jacobi Polynomials 5. Haar's Orthogonal System 7. Rademacher's and Walsh's Orthogonal Systems. General Summation Processes 2. The Abel Transform. Some Tauberian Theorems 3. Everywhere Divergent Orthogonal Series 5.
Convergence with Every Arrangement of the Terms 6. Menchoff's Summation Theorem Multiplicatively Orthogonal Systems. Generalization of the Walsh Series 3. Banach Spaces.
Functionals 2. The Singular Integrals 3.
On the convergence of orthogonal series - PDF Free Download
Generalities on the Degree of Approximation 6. Approximation Properties of Some Orthogonal Systems 7. Structural Convergence Conditions 8.
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