AN INTRODUCTION TO HARMONIC ANALYSIS

By L. KALIT

CONTENTS I FOURIER SERIES ON T FOURIER COEF?CIENTS SUMMABILITY IN NORM AND HOMOGENEOUS BANACH SPACES ON T POINTWISE CONVERGENCE OF ?N(F) THE ORDER OF MAGNITUDE OF FOURIER COEF?CIENTS FOURIER SERIES OF SQUARE SUMMABLE FUNCTIONS ABSOLUTELY CONVERGENT FOURIER SERIES FOURIER COEF?CIENTS OF LINEAR FUNCTIONALS ADDITIONAL COMMENTS AND APPLICATIONS II THE CONVERGENCE OF FOURIER SERIES CONVERGENCE IN NORM CONVERGENCE AND DIVERGENCE AT A POINT SETS OF DIVERGENCE III THE CONJUGATE FUNCTION THE CONJUGATE FUNCTION THE MAXIMAL FUNCTION OF HARDY AND LITTLEWOOD THE HARDY SPACES IV INTERPOLATION OF LINEAR OPERATORS INTERPOLATION OF NORMS AND OF LINEAR OPERATORS THE THEOREM OF HAUSDORFF-YOUNG V LACUNARY SERIES AND QUASI-ANALYTIC CLASSES LACUNARY SERIES QUASI-ANALYTIC CLASSES VI FOURIER TRANSFORMS ON THE LINE FOURIER TRANSFORMS FOR L1(R) FOURIER-STIELTJES TRANSFORMS FOURIER TRANSFORMS IN LP(R); 1 < P ?2 TEMPERED DISTRIBUTIONS AND PSEUDO-MEASURES ALMOST-PERIODIC FUNCTIONS ON THE LINE THE WEAK-STAR SPECTRUM OF BOUNDED FUNCTIONS THE PALEY–WIENER THEOREMS THE FOURIER-CARLEMAN TRANSFORM KRONECKER’S THEOREM VII FOURIER ANALYSIS ON LOCALLY COMPACT ABELIAN GROUPS LOCALLY COMPACT ABELIAN GROUPS THE HAAR MEASURE CHARACTERS AND THE DUAL GROUP FOURIER TRANSFORMS ALMOST-PERIODIC FUNCTIONS AND THE BOHR COMPACTI?CATION VIII COMMUTATIVE BANACH ALGEBRAS DE?NITION, EXAMPLES, AND ELEMENTARY PROPERTIES MAXIMAL IDEALS AND MULTIPLICATIVE LINEAR FUNCTIONALS THE MAXIMAL-IDEAL SPACE AND THE GELFAND REPRESENTATION HOMOMORPHISMS OF BANACH ALGEBRAS REGULAR ALGEBRAS WIENER’S GENERAL TAUBERIAN THEOREM SPECTRAL SYNTHESIS IN REGULAR ALGEBRAS FUNCTIONS THAT OPERATE IN REGULAR BANACH ALGEBRAS THE ALGEBRA M(T) AND FUNCTIONS THAT OPERATE ON FOURIER-STIELTJES COEF?CIENTS THE USE OF TENSOR PRODUCTS