## A First Course in Functional Analysis: Theory and ApplicationsThis book provides the reader with a comprehensive introduction to functional analysis. Topics include normed linear and Hilbert spaces, the Hahn-Banach theorem, the closed graph theorem, the open mapping theorem, linear operator theory, the spectral theory, and a brief introduction to the Lebesgue measure. The book explains the motivation for the development of these theories, and applications that illustrate the theories in action. Applications in optimal control theory, variational problems, wavelet analysis and dynamical systems are also highlighted. ‘A First Course in Functional Analysis’ will serve as a ready reference to students not only of mathematics, but also of allied subjects in applied mathematics, physics, statistics and engineering. |

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### Contents

Normed Linear Spaces 5890 | 58 |

Hilbert Space 91129 | 91 |

Linear Operators 130178 | 130 |

Linear Functionals 179220 | 179 |

Space of Bounded Linear Functionals 221266 | 221 |

Closed Graph Theorem and Its Consequences 267281 | 267 |

Compact Operators on Normed Linear Spaces 282322 | 282 |

Elements of Spectral Theory of SelfAdjoint 323353 | 323 |

Unbounded Linear Operators 381399 | 381 |

The HahnBanach Theorem and Optimization 400409 | 400 |

Variational Problems 410429 | 410 |

The Wavelet Analysis 430442 | 430 |

Dynamical Systems 443453 | 443 |

List of Symbols 454458 | 454 |

463 | |

Measure and Integration in Lp Spaces 354380 | 354 |

### Other editions - View all

A First Course in Functional Analysis: Theory and Applications Rabindranath Sen Limited preview - 2014 |

A First Course in Functional Analysis: Theory and Applications Rabindranath Sen No preview available - 2012 |

### Common terms and phrases

adjoint arbitrary axioms Banach space bounded linear operator bounded variation called Cauchy sequence closed subspace compact linear operator compact operator complete conjugate continuous function convex set countable defined Deﬁnition denoted differential eigenvalue element equation everywhere dense Ex and Ey example exists ﬁnd finite dimensional ﬁrst ﬁxed follows Fourier functional deﬁned functional f given Hahn-Banach theorem Hence Hilbert space iI1 iI1 implies inequality inﬁnite inner product space integral Let Ex Let f Let us consider linear operator mapping linearly independent llfll llwll metric space n-dimensional neighbourhood non-zero normed linear space open ball open set orthogonal orthonormal system polynomials problem Proof prove rational numbers real numbers reﬂexive satisﬁes scalar self-adjoint operator solution space Ex space H subset Theorem Let topological space unique vector wavelet matrix weakly zero