From 777f9d3fd8caf56e6bc6999a4b05379307d0733f Mon Sep 17 00:00:00 2001
From: Justin Gassner <justin.gassner@mailbox.org>
Date: Tue, 12 Sep 2023 07:36:33 +0200
Subject: Initial commit

---
 pages/distribution-theory/definitions.md    |  9 +++++++++
 pages/distribution-theory/index.md          | 26 ++++++++++++++++++++++++++
 pages/distribution-theory/sobolev-theory.md |  9 +++++++++
 3 files changed, 44 insertions(+)
 create mode 100644 pages/distribution-theory/definitions.md
 create mode 100644 pages/distribution-theory/index.md
 create mode 100644 pages/distribution-theory/sobolev-theory.md

(limited to 'pages/distribution-theory')

diff --git a/pages/distribution-theory/definitions.md b/pages/distribution-theory/definitions.md
new file mode 100644
index 0000000..a800e03
--- /dev/null
+++ b/pages/distribution-theory/definitions.md
@@ -0,0 +1,9 @@
+---
+title: Definitions
+parent: Distribution Theory
+nav_order: 10
+# cspell:words
+published: false
+---
+
+# {{ page.title }}
diff --git a/pages/distribution-theory/index.md b/pages/distribution-theory/index.md
new file mode 100644
index 0000000..b4b50a8
--- /dev/null
+++ b/pages/distribution-theory/index.md
@@ -0,0 +1,26 @@
+---
+title: Distribution Theory
+nav_order: 3
+has_children: true
+has_toc: false
+published: true
+---
+
+# {{ page.title }}
+
+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.
diff --git a/pages/distribution-theory/sobolev-theory.md b/pages/distribution-theory/sobolev-theory.md
new file mode 100644
index 0000000..931731f
--- /dev/null
+++ b/pages/distribution-theory/sobolev-theory.md
@@ -0,0 +1,9 @@
+---
+title: Sobolev Theory
+parent: Distribution Theory
+nav_order: 10
+# cspell:words
+published: false
+---
+
+# {{ page.title }}
-- 
cgit v1.2.3-70-g09d2