Mehdi
Radjabalipour,
Iranian
Academy
of
Sciences
“Algebraic
frames”
The
theory
of
frames
(ordinary,
generalized,
analytic
or
algebraic
frames)
is
a
setting
in
which
one
can
study
signal
processing
tools
such
as:
Fourier
series,
Fourier
transform,
win-dowed
Fourier
transform,
continuous
wavelet
transforms,
etc.
Signals
are
viewed
as
elements
of
a
separable
complex
Hilbert
space
and
the
processing
can
be
viewed
as
application
of
a
rather
rich
class
of
linear
functionals
on
these
signals.
The
frames
can
be
divided
into
two
types
of
analytic
or
algebraic
frames
depending
on
whether
the
linear
functionals
involved
are
bounded
(like
in
the
case
of
Fourier
transforms
on
compact
abelian
groups)
or
unbounded
(like
in
the
case
of
locally
compact
abelian
groups).
The
transformation
implementing
the
signal
processing,
called
the
analysis
operator,
may
be
a
bounded
or
an
unbounded
operator
on
the
signal
space.
The
aim
of
this
talk
is
to
study
the
operator
theoretic
aspects
of
the
frame
theory
arising
from
the
analysis
operator
and
its
inverse,
called
the
synthesis
operator.