Spectral theory is an extremely rich field which has found its application in many
areas of physics and mathematics. One of the reason which makes it so attractive is that it provides a unifying framework for problems in
various branches of mathematics, for example partial differential equations, calculus of variations, geometry, etc. Spectral theory came to
prominence when quantum mechanics was introduced in modern physics. In quantum mechanics classical quantities (position, momentum, ...)
are represented by (bounded, unbounded, self-adjoint, ...) operators. The eigenvalues of these operators are the only precise measurements of
the quantity. This course introduces the fundamentals of such operators and the space of their eigenvalues, which is called the (discrete,
continuous, ...) spectrum. |
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