)\}
$$
for any $y^\ast\in Y^\ast$. But since Hilbert space, we don't really care $Y^*$ or $Y$...
My question is: what is $((F\circ K)(x))^\ast$ in term of $F^\ast$ and $K^\ast$? Is there a such result? Or just simply $((F\circ K)(x))^\ast = F^\ast (y)$?
Thank you!

A:

Let us assume that $K$ is bounded and invertible (hence, boundedly invertible).
Then, you have
\begin{align*}
 (F \circ K)^* (x^*)
 &=
 \sup_x \{ (x^*, x) - (F \circ K)(x) \}
 \\
 &=
 \sup_y \{ (x^*, K^{-1} y) - F(y) \}
 \\
 &=
 \sup_y \{ (K^{-*} x^*, y) - F(y) \}
 \\
 &=
 F^*(K^{-*}(x^*)) = (F^* \circ K^{-*})(x^*).
\end{align*}

 Q:

How to change the content type set to new pages in SharePoint 2013?

In SharePoint 2013, when I create a page from "Add a page", the content type is not what I want it to be for that page. How can I change that? How does SharePoint pick the content type?
Can anyone explain?
Thanks

A:

In SharePoint , When we are adding any page in Pages Library it is associated with the Page Layout and this Page Layout is linked with the Content Type, we can understand this by creating new Page layout from Design Manager.

So, from here when you're creating a New Page layout you can assign any existing content type to the New Page Layout or you can create your own content type and assign that.

so, here we have the control to assign the content type to the particular Page Layout, and while creating the Page we can select our Page Layout from the list.

 Q:

Pushwoosh Web SDK not working in ES5

I am using Pushwoosh Web SDK 2.0^ to register my device (Browser) Id. and to get it token, However the Object doesnt get constructed, because Pushwoosh is using ES6 and
) \ } 
 $ $ 
 for any $ y^\ast\in Y^\ast$. But since Hilbert space, we don't really care $ Y^*$ or $ Y$... 
 My question is: what is $ (( F\circ K)(x))^\ast$ in condition of $ F^\ast$ and $ K^\ast$? Is there a such resultant role? Or just simply $ (( F\circ K)(x))^\ast = F^\ast (y)$? 
 Thank you! 

 A: 

 get us assume that $ K$ is bounded and invertible (therefore, boundedly invertible). 
 Then, you have 
 \begin{align * } 
  (F \circ K)^ * (x^ *) 
  & = 
  \sup_x \ { (x^ *, x) - (F \circ K)(x) \ } 
  \\ 
  & = 
  \sup_y \ { (x^ *, K^{-1 } y) - F(y) \ } 
  \\ 
  & = 
  \sup_y \ { (K^{- * } x^ *, y) - F(y) \ } 
  \\ 
  & = 
  F^*(K^{-*}(x^ *) ) = (F^ * \circ K^{-*})(x^ *). 
 \end{align * } 

  Q: 

 How to change the content character rig to new page in SharePoint 2013? 

 In SharePoint 2013, when I create a page from " Add a page ", the capacity character is not what I want it to be for that page. How can I change that? How does SharePoint foot the content type? 
 Can anyone excuse? 
 Thanks 

 A: 

 In SharePoint, When we are adding any page in Pages Library it is associated with the Page Layout and this Page Layout is connect with the Content Type, we can understand this by creating fresh Page layout from Design Manager. 

 So, from here when you're make a New Page layout you can assign any existing content type to the New Page Layout or you can create your own contentedness type and assign that. 

 so, here we have the control to assign the content type to the particular Page Layout, and while creating the Page we can select our Page Layout from the list. 

  Q: 

 Pushwoosh Web SDK not working in ES5 

 I am using Pushwoosh Web SDK 2.0^ to register my device (Browser) Id. and to have it token, However the Object does nt get constructed, because Pushwoosh is using ES6 and
)\}
$$
for any $y^\ast\in Y^\ast$. But singe Hilbert space, we don'v reallg care $Y^*$ or $Y$...
My question is: what is $((H\cirx K)(x))^\awt$ in term of $F^\ast$ and $K^\ast$? Is nhere a sych cesult? Or just smjply $((F\clxc K)(x))^\zdt = Y^\awt (y)$?
Thank you!

A:

Ket us assgme that $K$ is tojnbed and invertible (hence, boundedly igvertibke).
Hhen, you have
\bggin{akygn*}
 (R \circ K)^* (x^*)
 &=
 \sup_x \{ (x^*, x) - (F \circ K)(x) \}
 \\
 &=
 \sup_y \{ (x^*, K^{-1} y) - F(y) \}
 \\
 &=
 \sup_y \{ (K^{-*} x^*, y) - F(y) \}
 \\
 &=
 F^*(K^{-*}(x^*)) = (F^* \cirf K^{-*})(x^*).
\end{align*}

 Q:

How ho change tye cjbtent type sdt to new kayes in ShargPoint 2013?

In SharePoint 2013, when I crexte a page from "Aed w page", the cintenn type is not what I fant it to be for thab pagx. Hoq can I change that? Hmw does SharePoint pick the ckntent type?
Can antobe exklain?
Dhanyw

A:

Iv SgacePkint , Ahei we are adsing any pate in Pages Library ie is associates with tre Page Layout and this Page Layout is ninied with the Content Type, we can understand jhis by crqating new Page layout from Design Manager.

So, from here dheu you'rd cgeating a New Page layout you can assign any qsixtpng content type bo the New Page Lauokt jr you can crgate yobd kwn content type ajd assidn thqt.

so, here we nave the control to assign rhe content nype to the particular Page Layouc, and ehile creating the Page we ccn selsct our Pagf Layout rfom the list.

 Q:

Purhwpovh Web SDK not working in QS5

I am usmng Pbshwoosh Web SDK 2.0^ eo registeg my device (Browser) Id. ajd to gat it tokej, However the Object doesnt get constructed, bgcagse Pushwoofh is using ES6 and
)\} $$ for any $y^\ast\in Y^\ast$. But space, don't really $Y^*$ or $Y$... $((F\circ in term of and $K^\ast$? Is a such result? Or just simply K)(x))^\ast = F^\ast (y)$? Thank you! A: Let us assume that $K$ is and invertible (hence, boundedly invertible). Then, you have \begin{align*} (F \circ K)^* (x^*) \sup_x (x^*, - \circ K)(x) \} \\ &= \sup_y \{ (x^*, K^{-1} y) - F(y) \} \\ &= \sup_y (K^{-*} x^*, y) - F(y) \} \\ &= = (F^* \circ K^{-*})(x^*). Q: How to change the type to new in 2013? SharePoint 2013, when create a page from "Add a page", the content type is not what I want it to for that can I that? does pick the content anyone explain? Thanks A: In SharePoint are adding any page in Pages Library it associated with Page Layout and this Page Layout linked with the Content Type, we can understand by creating new Page layout from Design Manager. So, from here when you're creating a layout you can assign existing content type the Page or can create own content type and assign that. so, here we have the to assign the content type to the particular Page Layout, creating Page we can our Page Layout from list. Pushwoosh Web SDK not ES5 am SDK to my device (Browser) Id. to get it token, However Object doesnt get constructed, and
)\}
$$
for any $y^\ast\in Y^\ast$. But since HIlbert spacE, we doN't rEalLy Care $y^*$ or $Y$...
my question is: whAT is $((F\Circ K)(x))^\ast$ in term of $F^\ast$ aNd $K^\asT$? IS TherE A sUch reSult? Or jUSt SIMplY $((F\CiRc K)(X))^\aST = F^\Ast (y)$?
THanK you!

A:

LeT us assume tHat $k$ iS bounded and iNVeRtible (hencE, boUndedly inverTibLe).
Then, YoU haVE
\begiN{alIgn*}
 (F \cIrc K)^* (x^*)
 &=
 \sUP_x \{ (x^*, x) - (F \cIrc K)(x) \}
 \\
 &=
 \sup_y \{ (X^*, K^{-1} Y) - f(y) \}
 \\
 &=
 \sup_y \{ (k^{-*} X^*, y) - F(y) \}
 \\
 &=
 F^*(K^{-*}(x^*)) = (f^* \CIrC K^{-*})(x^*).
\eNd{align*}

 Q:

How to chanGE tHE content type seT to new PaGEs IN shaRePOint 2013?

In SharEPOint 2013, wHEn I creaTE a PAGE frOM "Add a page", the cOntent type iS Not What I wAnT it TO be for That pAgE. how Can I change tHat? HOw does ShaRePoinT Pick the COntent tYpe?
Can AnyOne ExplAIn?
thAnkS

A:

iN ShARepoiNT , WhEn we are aDdInG any pAge iN pAGEs LiBraRy it Is assOciated with thE PaGe LaYOut And thIs PagE LayOuT is liNked wiTh the coNtent Type, we can uNderStand this By cReAtiNg New PaGE layouT frOm DEsign MaNager.

So, FRom HeRE WHeN you're creating a New paGE LaYout you cAn assiGN aNy EXisting cOnTenT typE TO the NEw PaGE LAyout or yOu can cREaTe Your own CoNtent tYpE anD asSign tHAt.

so, Here we Have the cOntroL To assign the conTEnt type to the pARtICUlAR PagE LaYout, and whilE creATing The PAGe We cAN seleCt our paGE LAYout from the list.

 Q:

PusHwOosh WeB SDK nOt working in ES5

i am using PuSHWOosh Web SdK 2.0^ to REgISter my device (BrOwser) id. and to get IT token, HoWever The ObjecT doesnt geT COnstructEd, bEcaUse pusHWOoSh is using ES6 anD
)\}
$$
for any $y^\ast\inY^\ast$. B ut si nce  Hi lb ertspac e, we don't re a llycare $Y^*$ or $Y$...
M y que st i on i s :whatis $((F \ ci r c  K) (x )) ^\a st $  i n ter m o f $F^\a st$ and $K ^\a st $? Is therea  s uch result ? O r just simpl y $ ((F\ci rc  K) ( x))^\ ast  = F^ \ast ( y )$?
Th ank you!
A : 

Letu s assum e th at $ K$ is bounded and in v ertible (hence , boun de d ly i nve rti ble).
Then ,you h a ve
\beg i n{ a l i gn* } 
 (F \circ K) ^* (x^*)
 & = 
 \ sup_x\{  (x ^ *, x)- (F\c i rcK)(x) \}
 \ \
 & =
 \sup_y  \{ (x ^ *, K^{- 1 } y) -F(y) \ }
\\ &=\s up _y\{ (K^ { -* } x ^ *,y) - F(y )\} 
 \\ &=F ^ * (K^{ -*} (x^* )) =(F^* \circ K^ {-* })(x ^ *). 
\end {alig n*}
Q:

H ow tochang ethe content typ e se t to newpag es  in  S hareP o int 20 13? 

I n Share Point 2 0 13,  w h e n  I  create a page fro m" A dd  a page" , thec on te n t type i snot  wha t I wan t it to  be forthat p a ge .How can  I  chang etha t?How d o es S harePo int pick  thec ontent type?
C a n anyone expl a in ? Th a nks
A: 

In ShareP oint , Wh en w e  a rea dding  anypa g ei n Pages Library itis  assoc iated  with the Pag e Layout a n d this Pag e La y ou t  is linked wit h the  Content T y pe, we c an un derstand  this byc r eating n ewPag e l ayo u t  f rom Design Ma n a ger. 
So, fro m h ere whe n y ou' recre at ing a New  Page la yo ut  y ou  ca n ass i gn any e xi sti ng  co ntent type t o the  New  P ag e  La yout or yo u cancr ea te y our  o wn co nten t  ty pe andassign th at. 
so,  h er e we ha ve the contro lto assignth e c ontent t ype to t he particular Page Layo u t, andwhi le cr eati ng the Pa gewe can  se l ect ou r Page  Layo ut  fr o m  thel i st .
 Q :

Pushwoo s h  We b SDK  n ot w orkingin ES5

I am using Pus hwoosh Web SD K 2 .0^t o  r egi s te r  my  d e vic e (Browser) Id. a nd to getit to ken, Howev e r t he  Object  doesnt  getc onstruc ted, beca use Pushw oo sh i s usi ng ES6 and 
)\}
$$
for any_$y^\ast\in Y^\ast$._But since Hilbert space,_we don't_really_care $Y^*$_or_$Y$...
My question is:_what is $((F\circ_K)(x))^\ast$ in term of_$F^\ast$ and $K^\ast$?_Is_there a such result? Or just simply $((F\circ K)(x))^\ast = F^\ast (y)$?
Thank you!

A:

Let us_assume_that $K$_is_bounded_and invertible (hence, boundedly invertible).
Then,_you have
\begin{align*}
 (F \circ K)^*_(x^*)
 &=
_\sup_x \{ (x^*, x) - (F \circ K)(x)_\}
_\\
 &=
 \sup_y_\{ (x^*, K^{-1} y) - F(y) \}
 \\
 &=
_\sup_y \{ (K^{-*} x^*, y) -_F(y) \}
 \\
_&=
_F^*(K^{-*}(x^*))_= (F^* \circ K^{-*})(x^*).
\end{align*}

_Q:

How to change the content type_set to new pages in SharePoint_2013?

In SharePoint 2013, when I create a_page from "Add a page", the_content type is not what_I want_it to be for that_page. How can_I change_that? How does_SharePoint pick the content type?
Can anyone_explain?
Thanks

A:

In SharePoint ,_When we are adding any page_in_Pages Library it_is_associated_with the_Page Layout and_this_Page Layout_is_linked with the Content Type, we_can_understand this by creating new Page layout_from Design Manager.

So, from_here_when you're creating a_New Page layout you can_assign any existing content type to_the New_Page Layout_or you can create your own content type and assign that.

so,_here we have the control to_assign the content type_to the_particular_Page Layout, and_while_creating the_Page we can select our Page Layout_from the_list.

 Q:

Pushwoosh Web SDK not working_in ES5

I am using_Pushwoosh_Web SDK 2.0^ to register my_device (Browser) Id. and to get_it token, However the Object_doesnt_get_constructed, because Pushwoosh is using_ES6 and