## The Selected Works of V.S. VaradarajanV.S. Varadarajan has made significant contributions to a remarkably broad range of mathematical subjects which include probability theory, various mathematical aspects of quantum mechanics, harmonic analysis on reductive groups and symmetric spaces, and the modern theory of meromorphic differential equations. The papers included in this volume have been selected to highlight these contributions. For other wonderful titles written by this author see: ""Euler through Time: A New Look at Old Themes"", ""Supersymmetry for Mathematicians: An Introduction"", ""The Mathematical Legacy of Harish-Chandra: A Celebration of Representation Theory and Harmonic Analysis"", and ""Algebra in Ancient and Modern Times"". |

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### Contents

Introduction 162 | 12 |

General properties of spaces of measures 181 | 31 |

Applications to rings of functions and function spaces 211 | 61 |

63 Path integrals for a class of Padic Schrodinger equations Lett Math | 63 |

Bibliography 227 | 77 |

14 Probability in physics and a theorem on simultaneous observability | 79 |

15 with C Radhakrishna Rao Discrimination of Gaussian Processes | 109 |

18 with K R Parthasarathy and R Ranga Rao Representations of complex | 167 |

19 On the ring of invariant polynomials on a semisimple Lie algebra Amer | 215 |

20 with P C Trombi Spherical transforms on semisimple Lie groups | 408 |

Acknowledgments | 629 |

21 with P C Trombi Asymptotic behaviour of eigen functions on a semi | 630 |

### Common terms and phrases

Amer analytic arbitrary assertion assume asymptotic Banach Borel sets Borel space bounded Cartan completely regular Consequently constant continuous functions convergence Corollary corresponding countable defined deformation denote differential equations dimensional direct sum distributions eigenvalues elements equivalent ergodic measures estimate exists finite fixed follows formula G-space Gaussian measures given Haar measure Harish-Chandra Hausdorff space hence Hilbert space homomorphism implies induction integer invariant measure irreducible isomorphism Lemma Lie algebra linear functional Math matrix metric space module Moreover nilpotent non-zero notation observable obtain Poincare group polynomial positive system probability measure Proof properties Proposition quantum r-algebra r-smooth relatively compact Remark representation of G resp result roots self-adjoint semisimple Lie groups separable metric space shows signed measure spherical functions subgroup subset subspace Suppose symmetric Theorem theorem is proved theory topological space topology transform unique Varadarajan vector weight write