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Title of Journal: Monatsh Math

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Abbravation: Monatshefte für Mathematik

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Springer Vienna

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DOI

10.1007/978-1-4899-7657-4_1

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1436-5081

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On matrix valued square integrable positive defini

Authors: Hongyu He
Publish Date: 2015/01/21
Volume: 177, Issue: 3, Pages: 437-449
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Abstract

In this paper we study matrix valued positive definite functions on a unimodular group We generalize two theorems of Godement on L2 positive definite functions We show that a matrixvalued continuous L2 positive definite function can always be written as the convolution of a matrixvalued L2 positive definite function with itself We also prove that given two L2 matrix valued positive definite functions Phi and Psi int G TrPhi g overlinePsi gt d g ge 0 In addition this integral equals zero if and only if Phi Psi =0 Our proofs are operatortheoretic and independent of the group

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Other Papers In This Journal:
  1. A central limit theorem for integer partitions
  2. Fully commutative elements in finite and affine Coxeter groups
  3. On semi-rational finite simple groups
  4. Integer-valued polynomials over matrices and divided differences
  5. On mean values of multiplicative functions on the symmetric group
  6. Simple exceptional groups of Lie type are determined by their character degrees
  7. Löwner chains with complex leading coefficient
  8. On a functional equation related to derivations in prime rings
  9. Ricci solitons and odd-dimensional spheres
  10. Regularity properties of distributions through sequences of functions
  11. An explicit growth condition for middle-degree cuspidal cohomology of arithmetically defined quaternionic hyperbolic n -manifolds
  12. Operations with monotone operators and the monotonicity of the resulting operators
  13. Normal families of meromorphic functions and shared values
  14. Some New Results on the Chu Duality of Discrete Groups
  15. Cauchy integral and singular integral operator over closed Jordan curves
  16. The zero-free region of the derivative of Selberg zeta functions
  17. A note on Engel words of finite groups
  18. Equivalence of plurisubharmonic singularities and Siu-type metrics
  19. Palindromic Prefixes and Diophantine Approximation
  20. Effective uniqueness of Parry measure and exceptional sets in ergodic theory
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