Principles of Fourier Analysis, 2nd Edition

34

Sequences and Series of Generalized Functions

Various sequences and infinite series of generalized functions will be appearing in the next several chapters. We will find them useful in describing many generalized functions that cannot be viewed as classical functions (delta functions, for example), and they can be used to extend some classical formulas to formulas that cannot be derived using the classical theory alone. Furthermore, the elements of one particularly important class of generalized functions are all infinite series of delta functions. These are the “arrays of delta functions”, and they will play major roles in at least three subsequent chapters.

34.1  Sequences and Limits

Limits of Sequences of Generalized Functions

Suppose ...