diff options
Diffstat (limited to 'pages/distribution-theory')
| -rw-r--r-- | pages/distribution-theory/definitions.md | 1 | ||||
| -rw-r--r-- | pages/distribution-theory/index.md | 29 | ||||
| -rw-r--r-- | pages/distribution-theory/sobolev-theory.md | 1 |
3 files changed, 14 insertions, 17 deletions
diff --git a/pages/distribution-theory/definitions.md b/pages/distribution-theory/definitions.md index a800e03..405eff2 100644 --- a/pages/distribution-theory/definitions.md +++ b/pages/distribution-theory/definitions.md @@ -2,7 +2,6 @@ title: Definitions parent: Distribution Theory nav_order: 10 -# cspell:words published: false --- diff --git a/pages/distribution-theory/index.md b/pages/distribution-theory/index.md index b4b50a8..3055c8f 100644 --- a/pages/distribution-theory/index.md +++ b/pages/distribution-theory/index.md @@ -1,6 +1,6 @@ --- title: Distribution Theory -nav_order: 3 +nav_order: 5 has_children: true has_toc: false published: true @@ -10,17 +10,16 @@ published: true As usual, let $\mathcal{S}$ denote the space of Schwartz test functions on $\RR^n$. -{: .definition-title } -> Definition (Operator Valued Distribution) -> -> Let $\hilb{H}$ be a Hilbert space. -> An *operator valued tempered distribution* $\Phi$ (on $\RR^n$) -> is a mapping that associates to each test function $f \in \mathcal{S}$ -> an unbounded linear operator $\Phi(f)$ in $\hilb{H}$ such that -> {: .mb-0 } -> -> {: .my-0 } -> - there is a dense linear subspace $\mathcal{D}$ of $\hilb{H}$ that -> is contained in the domain of all the $\Phi(f)$ -> - for every fixed pair of vectors $\phi, \psi \in \hilb{D}$ -> the mapping $f \mapsto \innerp{\phi}{\Phi(f) \psi}$ is a tempered distribution. +{% definition Operator Valued Distribution %} +Let $\hilb{H}$ be a Hilbert space. +An *operator valued tempered distribution* $\Phi$ (on $\RR^n$) +is a mapping that associates to each test function $f \in \mathcal{S}$ +an unbounded linear operator $\Phi(f)$ in $\hilb{H}$ such that +{: .mb-0 } + +{: .my-0 } +- there is a dense linear subspace $\mathcal{D}$ of $\hilb{H}$ that +is contained in the domain of all the $\Phi(f)$ +- for every fixed pair of vectors $\phi, \psi \in \hilb{D}$ +the mapping $f \mapsto \innerp{\phi}{\Phi(f) \psi}$ is a tempered distribution. +{% enddefinition %} diff --git a/pages/distribution-theory/sobolev-theory.md b/pages/distribution-theory/sobolev-theory.md index 931731f..d7a91e2 100644 --- a/pages/distribution-theory/sobolev-theory.md +++ b/pages/distribution-theory/sobolev-theory.md @@ -2,7 +2,6 @@ title: Sobolev Theory parent: Distribution Theory nav_order: 10 -# cspell:words published: false --- |