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this is an educational question.

can someone please explain with some simple examples:

(1) what is/are the spectrum of operator

(2) where it is useful

For providing examples of spectrum of operator, please also consider the following operator, matrix (A), differential operator, integral operator, .....

thank u.

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    First, see http://en.wikipedia.org/wiki/Spectrum_(functional_analysis)2011-03-28
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    Dear Mozo, you've asked several somewhat poorly motivated questions in a short span of time that, in many ways, ask the answerer to do your work for you. Please be aware that this is generally bad etiquette to ask questions in this manner (especially since you have not accepted any answers yet).2011-03-28
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    @Mathew. Dear Akhil, i think that one of the most motivational aspects of knowledge is to know its usefulness. And, that is my second question. As for as as accepting answer is concerned. I am still looking for a simple answer with simple examples. For example, spectrum of $d/dx$ and its usage. And, the most important of all I very much appreciate efforts of everyone who are trying to answer my questions. I do.2011-03-28

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