Mixing
Higher order functional analysis?
$begingroup$
Is there a theory of higher order functional analysis?
i.e. Instead of taking function spaces, taking functional or operator spaces?
What would this subject be called and are there any known results in it?
Perhaps if function space is like an infinite vector space. Then an example of the higher order (linear) function space would be a like an infinite matrix space? And for the non-linear case it would be a space of infinite dimensional tensors of all orders?
functional-analysis
asked Jan 3 at 5:23
zoobyzooby
985616
$endgroup$
add a comment |
$begingroup$
Is there a theory of higher order functional analysis?
i.e. Instead of taking function spaces, taking functional or operator spaces?
What would this subject be called and are there any known results in it?
Perhaps if function space is like an infinite vector space. Then an example of the higher order (linear) function space would be a like an infinite matrix space? And for the non-linear case it would be a space of infinite dimensional tensors of all orders?
functional-analysis
asked Jan 3 at 5:23
zoobyzooby
985616
$endgroup$
$begingroup$
Not trying to sound cheeky, but functionals and operators are functions themselves, so why wouldn't functional analysis also apply to spaces composed of them?
$endgroup$
– ItsJustASeriesBro
Jan 3 at 5:29
$begingroup$
Not sure. But functionals are like functions of functions. They would be one order up in type-theory.
$endgroup$
– zooby
Jan 3 at 5:33
$begingroup$
Quadratic forms are also studied in Functional Analysis.
$endgroup$
– DisintegratingByParts
Jan 3 at 18:50
add a comment |
$begingroup$
Is there a theory of higher order functional analysis?
i.e. Instead of taking function spaces, taking functional or operator spaces?
What would this subject be called and are there any known results in it?
Perhaps if function space is like an infinite vector space. Then an example of the higher order (linear) function space would be a like an infinite matrix space? And for the non-linear case it would be a space of infinite dimensional tensors of all orders?
functional-analysis
asked Jan 3 at 5:23
zoobyzooby
985616
$endgroup$
Is there a theory of higher order functional analysis?
i.e. Instead of taking function spaces, taking functional or operator spaces?
What would this subject be called and are there any known results in it?
Perhaps if function space is like an infinite vector space. Then an example of the higher order (linear) function space would be a like an infinite matrix space? And for the non-linear case it would be a space of infinite dimensional tensors of all orders?
functional-analysis
functional-analysis
asked Jan 3 at 5:23
zoobyzooby
985616
asked Jan 3 at 5:23
zoobyzooby
985616
asked Jan 3 at 5:23
zoobyzooby
985616
asked Jan 3 at 5:23
zoobyzooby
985616
asked Jan 3 at 5:23
zoobyzooby
985616
985616
$begingroup$
Not trying to sound cheeky, but functionals and operators are functions themselves, so why wouldn't functional analysis also apply to spaces composed of them?
$endgroup$
– ItsJustASeriesBro
Jan 3 at 5:29
$begingroup$
Not sure. But functionals are like functions of functions. They would be one order up in type-theory.
$endgroup$
– zooby
Jan 3 at 5:33
$begingroup$
Quadratic forms are also studied in Functional Analysis.
$endgroup$
– DisintegratingByParts
Jan 3 at 18:50
add a comment |
$begingroup$
Not trying to sound cheeky, but functionals and operators are functions themselves, so why wouldn't functional analysis also apply to spaces composed of them?
$endgroup$
– ItsJustASeriesBro
Jan 3 at 5:29
$begingroup$
Not sure. But functionals are like functions of functions. They would be one order up in type-theory.
$endgroup$
– zooby
Jan 3 at 5:33
$begingroup$
Quadratic forms are also studied in Functional Analysis.
$endgroup$
– DisintegratingByParts
Jan 3 at 18:50
$begingroup$
Not trying to sound cheeky, but functionals and operators are functions themselves, so why wouldn't functional analysis also apply to spaces composed of them?
$endgroup$
– ItsJustASeriesBro
Jan 3 at 5:29
$begingroup$
Not trying to sound cheeky, but functionals and operators are functions themselves, so why wouldn't functional analysis also apply to spaces composed of them?
$endgroup$
– ItsJustASeriesBro
Jan 3 at 5:29
$begingroup$
Not sure. But functionals are like functions of functions. They would be one order up in type-theory.
$endgroup$
– zooby
Jan 3 at 5:33
$begingroup$
Not sure. But functionals are like functions of functions. They would be one order up in type-theory.
$endgroup$
– zooby
Jan 3 at 5:33
$begingroup$
Quadratic forms are also studied in Functional Analysis.
$endgroup$
– DisintegratingByParts
Jan 3 at 18:50
$begingroup$
Quadratic forms are also studied in Functional Analysis.
$endgroup$
– DisintegratingByParts
Jan 3 at 18:50
add a comment |
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$begingroup$
Not trying to sound cheeky, but functionals and operators are functions themselves, so why wouldn't functional analysis also apply to spaces composed of them?
$endgroup$
– ItsJustASeriesBro
Jan 3 at 5:29
$begingroup$
Not sure. But functionals are like functions of functions. They would be one order up in type-theory.
$endgroup$
– zooby
Jan 3 at 5:33
$begingroup$
Quadratic forms are also studied in Functional Analysis.
$endgroup$
– DisintegratingByParts
Jan 3 at 18:50